Determine the approximate radian measure, to the nearest hundredth.
\displaystyle
33^o
Determine the approximate radian measure, to the nearest hundredth.
\displaystyle
138^o
Determine the approximate radian measure, to the nearest hundredth.
\displaystyle
252^o
Determine the approximate radian measure, to the nearest hundredth.
\displaystyle
347^o
Determine the approximate degree measure, to the nearest tenth, for each angle.
1.24
Determine the approximate degree measure, to the nearest tenth, for each angle.
2.82
Determine the approximate degree measure, to the nearest tenth, for each angle.
4.78
Determine the approximate degree measure, to the nearest tenth, for each angle.
6.91
Determine the exact radian measure.
\displaystyle
75^o
Determine the exact radian measure.
\displaystyle
20^o
Determine the exact radian measure.
\displaystyle
12^o
Determine the exact radian measure.
\displaystyle
9^o
Determine the exact degree measure of each angle.
\displaystyle
\frac{2\pi}{5}
Determine the exact degree measure of each angle.
\displaystyle
\frac{4\pi}{9}
Determine the exact degree measure of each angle.
\displaystyle
\frac{7\pi}{12}
Determine the exact degree measure of each angle.
\displaystyle
\frac{11\pi}{18}
The turntable in a microwave oven rotates 12 times per minute while the oven is operating. Determine the angular velocity of the turntable in
a) degrees per second
b) radians per second
Turntables for playing vinyl records have four speeds, in revolutions per minute (rpm): 16, 33\frac{1}{3}, 45, and 78. Determine the angular velocity for each speed in
- degrees per second
Turntables for playing vinyl records have four speeds, in revolutions per minute (rpm): 16, 33\frac{1}{3}, 45, and 78. Determine the angular velocity for each speed in
- radians per second
Determine an exact value for each expression.
\displaystyle
\frac{\cot\frac{\pi}{4}}{\cos\frac{\pi}{3}\csc \frac{\pi}{2}}
Determine an exact value for each expression.
\displaystyle
\cos \frac{\pi}{6} \csc \frac{\pi}{3} + \sin \frac{\pi}{4}
A ski lodge is constructed with one side along a vertical
cliff such that it has a height of 15 m, as shown. Determine an exact measure for the base of the lodge, b.
Given that \cot \frac{2\pi}{7} = \tan z, first express \frac{2\pi}{7} as a difference between \frac{\pi}{2} and an angle, and then apply a cofunction identity to determine the measure of angle z.
Given that \cos \frac{5\pi}{9} = -\sin y, first express \frac{5\pi}{9} as a sum of \frac{\pi}{2} and an angle, and then apply a trigonometric identity to determine the measure of angle y.
Given that \tan\frac{4\pi}{9} \doteq 5.6713, determine the following, to four decimal places, without using a calculator. Justify your answers.
\displaystyle
\cot \frac{\pi}{18}
Given that \tan\frac{4\pi}{9} \doteq 5.6713, determine the following, to four decimal places, without using a calculator. Justify your answers.
\displaystyle
\tan \frac{13\pi}{9}
Given that \tan \sin x = \cos \frac{3\pi}{11} and that x lies in the second quadrant, determine the measure of angle x.
Use an appropriate compound angle formula to express as a single trigonometric function, and then determine an exact value of each.
\displaystyle
\sin \frac{5\pi}{12}\cos\frac{\pi}{4} + \cos\frac{5\pi}{12}\sin\frac{\pi}{4}
Use an appropriate compound angle formula to express as a single trigonometric function, and then determine an exact value of each.
\displaystyle
\sin\frac{5\pi}{12} \cos \frac{\pi}{4} - \cos \frac{5\pi}{12} \sin \frac{\pi}{4}
Use an appropriate compound angle formula to express as a single trigonometric function, and then determine an exact value of each.
\displaystyle
\cos \frac{5\pi}{12}\cos \frac{\pi}{4} - \sin \frac{5\pi}{12} \sin \frac{\pi}{4}
Use an appropriate compound angle formula to express as a single trigonometric function, and then determine an exact value of each.
\displaystyle
\cos \frac{5\pi}{12} \cos \frac{\pi}{4} + \sin \frac{5\pi}{12} \sin \frac{\pi}{4}
Angles x and y are located in the first quadrant such that \sin x =\frac{4}{5} and \cos y = \frac{7}{25} .
- Determine an exact value for
\cos x.
Angles x and y are located in the first quadrant such that \sin x =\frac{4}{5} and \cos y = \frac{7}{25} .
- Determine an exact value for
\sin y.
Angles x and y are located in the first quadrant such that \sin x =\frac{4}{5} and \cos y = \frac{7}{25} .
- Determine an exact value for
\sin(x + y).
Angle x lies in the third quadrant, and \tanx = \frac{7}{24}.
a) Determine an exact value of \cos 2x.
b) Determine an exact value of \sin 2x.
Determine an exact value for \cos \frac{13\pi}{12}
Prove that
\displaystyle
\sin(2\pi -x ) = -\sin x
Prove that
\displaystyle
\sec x = \frac{2(\cos x \sin 2x - \sin x \cos 2x)}{\sin 2x}
Prove that
\displaystyle
2\sin x \cos y = \sin(x + y) + \sin(x - y)
Consider the equation \cos 2x = 2 \sin x \sec x. Either prove that it is an identity, or determine a counterexample to show that it is not an identity.
Prove that
\displaystyle
(\sin 2x)(\tan x + \cot x) =2