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Similar Question 1
<p>Determine exact expressions for the primary trigonometric ratios for <code class='latex inline'>270^{\circ}</code>.</p>
Similar Question 2
<p>One of the primary trigonometric ratios for an angle is given, as well as the quadrant in which the terminal arm lies. Find the other two primary trigonometry ratios. </p><p><code class='latex inline'>\displaystyle \tan C = -\frac{5}{12}</code>, fourth quadrant.</p>
Similar Question 3
<p>State all the angles between <code class='latex inline'>0^{\circ}</code> and <code class='latex inline'>360^{\circ}</code> that make each equation true.</p><p><code class='latex inline'>\tan 135^{\circ}</code> = -tan _____</p>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>The coordinates of a point on the terminal arm of an angle <code class='latex inline'>\theta</code> are shown. Determine the exact primary trigonometric ratios for <code class='latex inline'> \theta</code></p><p><code class='latex inline'>E(-1,-3)</code></p><img src="/qimages/823" />
<p>For each trigonometric ratio, use a sketch to determine in which quadrant the terminal arm of the principal angle lies, the value of the related acute angle <code class='latex inline'>\beta</code>, and the sign of the ratio.</p><p><code class='latex inline'>\text{tan }225^{\circ}</code></p>
<p>For each trigonometric ratio, use a sketch to determine in which quadrant the terminal arm of the principal angle lies, the value of the related acute angle <code class='latex inline'>\beta</code>, and the sign of the ratio.</p><p><code class='latex inline'>\sin 315^{\circ}</code></p>
<p>Sylvie drew a special triangle in quadrant 3 and determined that tan (180<code class='latex inline'>^{\circ}</code> + <code class='latex inline'>\theta</code>) = 1.</p><p><strong>(a)</strong> What is the value of angle <code class='latex inline'>\theta</code>?</p><p><strong>(b)</strong> What would be the exact value of tan $\theta$1, <code class='latex inline'>\cos \theta</code>, and <code class='latex inline'>\sin \theta</code>?</p>
<p>Use each trigonometric ratio to determine all values of <code class='latex inline'>\theta</code>, to the nearest degree if <code class='latex inline'>0^{\circ} \leq \theta \leq 360^{\circ}</code>.</p><p><code class='latex inline'>\sin\theta = 0.4815</code></p>
<p>Without using a calculator, determine two angles between <code class='latex inline'>0^{\circ}</code> and <code class='latex inline'>360^{\circ}</code> that have a cosine ratio of <code class='latex inline'>-\frac{\sqrt{3}}{2}</code>.</p>
<p>The coordinates of a point on the terminal arm of an angle <code class='latex inline'>\theta</code> are given. Determine the exact primary trigonometric ratios for <code class='latex inline'>\theta</code>.</p><p><code class='latex inline'>(-8, 6)</code></p>
<p>The coordinates of a point on the terminal arm of an angle <code class='latex inline'>\theta</code> are shown. Determine the exact primary trigonometric ratios for <code class='latex inline'> \theta</code></p><p><code class='latex inline'>C(-6,-8)</code></p><img src="/qimages/822" />
<p>For each trigonometric ratio, use a sketch to determine in which quadrant the terminal arm of the principal angle lies, the value of the related acute angle <code class='latex inline'>\beta</code>, and the sign of the ratio.</p><p><code class='latex inline'>\text{tan }110^{\circ}</code></p>
<p>State all the angles between <code class='latex inline'>0^{\circ}</code> and <code class='latex inline'>360^{\circ}</code> that make each equation true.</p><p><code class='latex inline'>\tan 135^{\circ}</code> = -tan _____</p>
<p>State all the angles between <code class='latex inline'>0^{\circ}</code> and <code class='latex inline'>360^{\circ}</code> that make each equation true.</p><p><code class='latex inline'>\cos</code> _____ = - <code class='latex inline'>\cos(-60^{\circ}</code>)</p>
<p>One of the primary trigonometric ratios for an angle is given, as well as the quadrant in which the terminal arm lies. Find the other two primary trigonometry ratios. </p><p><code class='latex inline'>\displaystyle \tan F = \frac{12}{7}</code>, first quadrant.</p>
<p>Determine exact expressions for the primary trigonometric ratios for <code class='latex inline'>270^{\circ}</code>.</p>
<p>For each trigonometric ratio, use a sketch to determine in which quadrant the terminal arm of the principal angle lies, the value of the related acute angle <code class='latex inline'>\beta</code>, and the sign of the ratio.</p><p><code class='latex inline'>\text{cos }285^{\circ}</code></p>
<p>Given angle <code class='latex inline'>\alpha</code>, where <code class='latex inline'>0^{\circ} \leq \alpha \leq 360^{\circ}</code>, <code class='latex inline'>\cos \alpha</code> is equal to a unique value. Determine the value of <code class='latex inline'>\alpha</code> to the nearest degree. Justify your answer.</p>
<p>One of the primary trigonometric ratios for an angle is given, as well as the quadrant in which the terminal arm lies. Find the other two primary trigonometry ratios. </p><p><code class='latex inline'>\displaystyle \cos B = \frac{3}{5}</code>, fourth quadrant.</p>
<p>Use the related acute angle to state an equivalent expression.</p><p><code class='latex inline'> \displaystyle \sin 350^{\circ} </code></p>
<ul> <li>i) For each angle <code class='latex inline'>\theta</code>, predict which primary trigonometric ratios are positive.</li> <li>ii) Determine the primary trigonometric ratios to the nearest hundredth.</li> </ul> <img src="/qimages/909" />
<p>The cosine of each of two angles between <code class='latex inline'>0^{\circ}</code> and <code class='latex inline'>360^{\circ}</code> is <code class='latex inline'>\frac{1}{\sqrt{2}}</code>. Determine the angles.</p>
<p>State all the angles between <code class='latex inline'>0^{\circ}</code> and <code class='latex inline'>360^{\circ}</code> that make each equation true.</p><p><code class='latex inline'>\tan 30^{\circ}</code> = tan _____</p>
<p>Determine another angle that has the same trigonometric ratios as each given angle. Draw a sketch with both angles labelled.</p><p><code class='latex inline'>\displaystyle \sin 100^{\circ}</code></p>
<p>One of the primary trigonometric ratios for an angle is given, as well as the quadrant in which the terminal arm lies. Find the other two primary trigonometry ratios. </p><p> <code class='latex inline'>\displaystyle \sin A = \frac{8}{17}</code>, first quadrant.</p>
<p>Write the trigonometric expression in terms acute angle the same ratio then state the exact value of the ratio.</p><p><code class='latex inline'> \displaystyle \sin(240^{\circ}) </code></p>
<p>Given each point <code class='latex inline'>P(x, y)</code> lying on the terminal arm of angle <code class='latex inline'>\theta</code>,</p> <ul> <li>i) State the value of <code class='latex inline'>\theta</code>, using both a counterclockwise and a clockwise rotation</li> <li>ii) determine the primary trigonometric ratios</li> </ul> <p><code class='latex inline'>P(-1,-1)</code></p>
<p>Determine the primary trigonometric ratios for each given angle.</p><p><code class='latex inline'>360^{\circ} </code></p>
<p>The coordinates of a point on the terminal arm of an angle <code class='latex inline'>\theta</code> are given. Determine the exact primary trigonometric ratios for <code class='latex inline'>\theta</code>.</p><p><code class='latex inline'>(1, 2)</code></p>
<p>Which of the following has the same trigonometric ratios as each given angle. Draw a sketch with both angles labelled.</p><p><code class='latex inline'>\displaystyle \cos 45^{\circ}</code></p>
<p><code class='latex inline'>W(-2, 7)</code> lies on the terminal arm of an angle in standard position. Determine exact expressions for the three primary trigonometric ratios for the angle.</p>
<p>The coordinates of a point on the terminal arm of an angle <code class='latex inline'>\theta</code> are given. Determine the exact primary trigonometric ratios for <code class='latex inline'>\theta</code>.</p><p><code class='latex inline'>(3, -5)</code></p>
<p><code class='latex inline'>V(5, -3)</code> lies on the terminal arm of an angle in standard position. Determine exact expressions for the three primary trigonometric ratios for the angle.</p>
<p><code class='latex inline'>\displaystyle \tan (\theta+\pi)=\tan \theta </code></p>
<p>Determine the exact primary trigonometric ratios for each angle. </p><p><code class='latex inline'>\displaystyle \angle E = 420^{\circ}</code></p>
<p>The side length of a rhombus is <code class='latex inline'>s</code>. One of its diagonals has the same length. Determine an exact expression for the length of the other diagonal.</p>
<p>Use the related acute angle to state an equivalent expression.</p><p><code class='latex inline'> \displaystyle \text{sin }160^{\circ} </code></p>
<p>The coordinates of a point on the terminal arm of an angle <code class='latex inline'>\theta</code> are given. Determine the exact primary trigonometric ratios for <code class='latex inline'>\theta</code>.</p><p><code class='latex inline'>(-15, -8)</code></p>
<p>Determine the exact primary trigonometric ratios for each angle. </p><p><code class='latex inline'>\displaystyle \angle F = -270^{\circ}</code></p>
<p>Determine the exact primary trigonometric ratios for each angle. </p><p><code class='latex inline'>\displaystyle \angle A = -45^{\circ}</code></p>
<p><code class='latex inline'>S(24, -7)</code> lies on the terminal arm of an angle in standard position. Determine exact expressions for the three primary trigonometric ratios for the angle.</p>
<p>Given angle <code class='latex inline'>\theta</code>, where <code class='latex inline'>0^{\circ} \leq \theta \leq 360^{\circ}</code>, determine two possible values of <code class='latex inline'>\theta</code> where each ratio would be true. Sketch both principal angles.</p><p><code class='latex inline'>\cos \theta = -0.2882</code> </p>
<p>Use each trigonometric ratio to determine all values of <code class='latex inline'>\theta</code>, to the nearest degree if <code class='latex inline'>0^{\circ} \leq \theta \leq 360^{\circ}</code>.</p><p> <code class='latex inline'>\cot</code> <code class='latex inline'>\theta = 8.1516</code></p>
<p>The coordinates of a point on the terminal arm of an angle <code class='latex inline'>\theta</code> are given. Determine the exact primary trigonometric ratios for <code class='latex inline'>\theta</code>.</p><p><code class='latex inline'>(6, -2)</code></p>
<p>Determine exact expressions for the primary trigonometric ratios for <code class='latex inline'>315^{o}</code>. </p>
<p>The coordinates of a point on the terminal arm of an angle <code class='latex inline'>\theta</code> are shown. Determine the exact primary trigonometric ratios for <code class='latex inline'> \theta</code></p><p><code class='latex inline'>D(2,5)</code></p><img src="/qimages/823" />
<p><code class='latex inline'>R(-8, 15)</code> lies on the terminal arm of an angle in standard position. Determine exact expressions for the three primary trigonometric ratios for the angle.</p>
<p>Determine the exact primary trigonometric ratios for each angle. </p><p><code class='latex inline'>\displaystyle \angle D = -315^{\circ}</code></p>
<p>Determine tow angles between <code class='latex inline'>0^o</code> and <code class='latex inline'>360^o</code> that have a secant of <code class='latex inline'>-\sqrt{2}</code>. Use a unit circle to help you. Do not use a calculator.</p>
<ul> <li>i) For each angle <code class='latex inline'>\theta</code>, predict which primary trigonometric ratios are positive.</li> <li>ii) Determine the primary trigonometric ratios to the nearest hundredth.</li> </ul> <img src="/qimages/911" />
<p>Determine any three positive angles that are co-terminal with <code class='latex inline'>120^{\circ}</code></p>
<p>The coordinates of a point on the terminal arm of an angle <code class='latex inline'>\theta</code> are shown. Determine the exact primary trigonometric ratios for <code class='latex inline'> \theta</code></p><p><code class='latex inline'>A(5, 12)</code></p><img src="/qimages/820" />
<p>One of the primary trigonometric ratios for an angle is given, as well as the quadrant in which the terminal arm lies. Find the other two primary trigonometry ratios. </p><p><code class='latex inline'>\displaystyle \cos E = -\frac{5}{6}</code>, second quadrant.</p>
<p>Determine the exact primary trigonometric ratios for each angle. </p><p><code class='latex inline'>\displaystyle \angle C = 540^{\circ}</code></p>
<p>State all the angles between <code class='latex inline'>0^{\circ}</code> and <code class='latex inline'>360^{\circ}</code> that make each equation true.</p><p>sin 45<code class='latex inline'>^{\circ}</code> = sin _____</p>
<p>Determine two angles between <code class='latex inline'>0^o</code> and <code class='latex inline'>360^o</code> that have a secant of -5.</p>
<p><code class='latex inline'>U(-2, -3)</code> lies on the terminal arm of an angle in standard position. Determine exact expressions for the three primary trigonometric ratios for the angle.</p>
<p>The coordinates of a point on the terminal arm of an angle <code class='latex inline'>\theta</code> are given. Determine the exact primary trigonometric ratios for <code class='latex inline'>\theta</code>.</p><p><code class='latex inline'>(3 -4)</code></p>
<p>Determine two angles between <code class='latex inline'>0^o</code> and <code class='latex inline'>360^o</code> that have a cotangent of -1. Use a unit circle to help you. Do not use a calculator.</p>
<p>Determine the exact primary trigonometric ratios for each angle. </p><p><code class='latex inline'>\displaystyle \angle B = - 120^{\circ}</code></p>
<p>One of the primary trigonometric ratios for an angle is given, as well as the quadrant in which the terminal arm lies. Find the other two primary trigonometry ratios. </p><p><code class='latex inline'>\displaystyle \tan C = -\frac{5}{12}</code>, fourth quadrant.</p>
<p>Determine the primary trigonometric ratios for each given angle.</p><p><code class='latex inline'> \displaystyle 180^{\circ} </code></p>
<p>Given cos <code class='latex inline'>\theta = - \frac{5}{12}</code>, where <code class='latex inline'>0^{\circ} \leq \theta \leq 360^{\circ}</code>, </p><p>(a) In which quadrant could the terminal arm of <code class='latex inline'>\theta</code> lie?</p><p>(b) Determine all possible primary trigonometric ratios for <code class='latex inline'>\theta</code>.</p><p>(c) Evaluate all possible values of <code class='latex inline'>\theta</code> to the nearest degree.</p>
<p>Express the following as a function of its related acute angle and evaluate.</p><p><code class='latex inline'> \displaystyle \sin 120^o </code></p>
<p>Determine any three negative angles that are co-terminal with <code class='latex inline'>330^{\circ}</code></p>
<p>The coordinates of a point on the terminal arm of an angle <code class='latex inline'>\theta</code> are shown. Determine the exact primary trigonometric ratios for <code class='latex inline'> \theta</code></p><p><code class='latex inline'>B(-3, 4)</code></p><img src="/qimages/821" />
<p>Based on your observations, copy and complete the table below to summarize the signs of the trigonometric ratios for a principal angle that lies in each of the quadrants.</p><img src="/qimages/908" />
<ul> <li>i) For each angle <code class='latex inline'>\theta</code>, predict which primary trigonometric ratios are positive.</li> <li>ii) Determine the primary trigonometric ratios to the nearest hundredth.</li> </ul> <img src="/qimages/912" />
<p><code class='latex inline'>\triangle PQR</code> has a right angle at <code class='latex inline'>Q</code>. If <code class='latex inline'>q = 17</code> cm and <code class='latex inline'>p = 15</code> cm, determine exact expressions for the three primary trigonometric ratios for <code class='latex inline'>\angle P</code>.</p>
<p>Determine two angles between <code class='latex inline'>0^o</code> and <code class='latex inline'>360^o</code> that have a cotangent of -3.</p>
<p>Determine exact expressions for the primary trigonometric ratios for <code class='latex inline'>120^{\circ}</code>.</p>
<p>Use the related acute angle to state an equivalent expression.</p><p><code class='latex inline'> \displaystyle \tan 110^o </code></p>
<p><code class='latex inline'>Q(-4, -3)</code> lies on the terminal arm of an angle in standard position. Determine exact expressions for the three primary trigonometric ratios for the angle.</p>
<p>Determine another angle that has the same trigonometric ratios as each given angle. Draw a sketch with both angles labelled.</p><p><code class='latex inline'>\displaystyle \cos 230^{\circ}</code></p>
<p>An acute angle <code class='latex inline'>\theta </code> has the point <code class='latex inline'>A(p, q)</code> on its terminal arm. </p> <ul> <li>Find an expression for the distance OA in terms of <code class='latex inline'>p</code> and <code class='latex inline'>q</code>.</li> </ul>
<p>Determine another angle that has the same trigonometric ratios as each given angle. Draw a sketch with both angles labelled.</p><p><code class='latex inline'>\displaystyle \sin 150^{\circ}</code></p>
<ul> <li>i) For each angle <code class='latex inline'>\theta</code>, predict which primary trigonometric ratios are positive.</li> <li>ii) Determine the primary trigonometric ratios to the nearest hundredth.</li> </ul> <img src="/qimages/910" />
<p>Determine another angle that has the same trigonometric ratios as each given angle. Draw a sketch with both angles labelled.</p><p><code class='latex inline'>\displaystyle \tan 350^{\circ}</code></p>
<p>Find the measure of an angle between 0° and 360° that is coterminal with the given angle.</p><p><code class='latex inline'>-149^o</code></p>
<p>Determine another angle that has the same trigonometric ratios as each given angle. Draw a sketch with both angles labelled.</p><p><code class='latex inline'>\displaystyle \tan 300^{\circ}</code></p>
<p>One of the primary trigonometric ratios for an angle is given, as well as the quadrant in which the terminal arm lies. Find the other two primary trigonometry ratios. </p><p><code class='latex inline'>\displaystyle \sin D = -\frac{2}{3}</code>, third quadrant.</p>
<p><code class='latex inline'>P(-5, 12)</code> lies on the terminal arm of an angle in standard position. Determine exact expressions for the three primary trigonometric ratios for the angle.</p>
<p>Use the related acute angle to state an equivalent expression.</p><p><code class='latex inline'> \displaystyle \text{cos }300^{\circ} </code></p>
<p>Determine the primary trigonometric ratios for each given angle.</p><p><code class='latex inline'>270^{\circ} </code></p>
<p>Two angles between <code class='latex inline'>0^{\circ}</code> and <code class='latex inline'>360^{\circ}</code> that have a tangent of <code class='latex inline'>-1</code>. Without using a calculator, determine the angles.</p>
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