Chapter Review Trig Ratios
Chapter
Chapter 5
Section
Chapter Review Trig Ratios
Solutions 24 Videos
• i) For each triangle, state the reciprocal trigonometric ratios for angle \theta.
• ii) Calculate the value of \theta to the nearest degree.
1.24mins
Q1a
• i) For each triangle, state the reciprocal trigonometric ratios for angle \theta.
• ii) Calculate the value of \theta to the nearest degree.
1.20mins
Q1b
• i) For each triangle, state the reciprocal trigonometric ratios for angle \theta.
• ii) Calculate the value of \theta to the nearest degree.
1.10mins
Q1c
• i) State the sign of each trigonometric ratio. Use a calculator to determine the value of each ratio.
• ii) For each trigonometric ratio, determine the principal angle and, where appropriate, the related acute angle. Then sketch another angle that has the equivalent ratio. Label the principal angle and the related acute angle on your sketch.

\displaystyle \tan (18^o) 

0.23mins
Q3a
• i) State the sign of each trigonometric ratio. Use a calculator to determine the value of each ratio.
• ii) For each trigonometric ratio, determine the principal angle and, where appropriate, the related acute angle. Then sketch another angle that has the equivalent ratio. Label the principal angle and the related acute angle on your sketch.

\displaystyle \sin (205^o) 

0.19mins
Q3b

i) State the sign of each trigonometric ratio. Use a calculator to determine the value of each ratio.

ii) For each trigonometric ratio, determine the principal angle and, where appropriate, the related acute angle. Then sketch another angle that has the equivalent ratio. Label the principal angle and the related acute angle on your sketch.

 \cos(-55^o) 

0.36mins
Q3c

For each sketch, state the primary trigonometric ratios associated with angle \theta. Express your answers in simplified radical form.

0.43mins
Q4a

For each sketch, state the primary trigonometric ratios associated with angle \theta. Express your answers in simplified radical form.

0.53mins
Q4b

For each sketch, state the primary trigonometric ratios associated with angle \theta. Express your answers in simplified radical form.

0.37mins
Q4c

Given \cos \phi = -\frac{7}{\sqrt{53}}, where 0^{\circ} \leq \phi \leq 360^{\circ}

(a) in which quadrant(s) does the terminal arm of angle \phi lie? Justify your answer.

(b) state the other five trigonometric ratios for angle \phi.

(c) calculate the value of the principal angle \phi to the nearest degree.

3.09mins
Q5

Determine whether the equation \cos \beta \cot \beta = \frac{1}{\sin \beta} - \sin \beta is an identity. State any restrictors on angle \beta.

2.14mins
Q6

Prove the identity. State any restrictions on the variables if all angles vary from 0^{\circ} to 360^{\circ}.

\tan \alpha \cos \alpha = \sin \alpha

0.15mins
Q7a

Prove the identity. State any restrictions on the variables if all angles vary from 0^{\circ} to 360^{\circ}.

\frac{1}{\cot \phi} = \sin \phi \sec \phi

0.31mins
Q7b

Prove the identity. State any restrictions on the variables if all angles vary from 0^{\circ} to 360^{\circ}.

1- \cos^2x = \frac{\sin x \cos x}{\cot x}

1.30mins
Q7c

Prove the identity. State any restrictions on the variables if all angles vary from 0^{\circ} to 360^{\circ}.

\sec \theta\cos \theta + \sec \theta \sin \theta = 1 + \tan \theta

0.26mins
Q7d

Determine whether it is possible to draw a triangle given each set of information. Sketch all possible triangles where appropriate. Calculate, then label, all side lengths to the nearest tenth of ta centimetre and all angles to the nearest degree.

b = 3.0 cm, c = 5.5 cm, \angle B = 30^{\circ}

3.56mins
Q8a

Determine whether it is possible to draw a triangle given each set of information. Sketch all possible triangles where appropriate. Calculate, then label, all side lengths to the nearest tenth of ta centimetre and all angles to the nearest degree.

b = 12.1 cm, c = 8.2 cm, \angle C = 34^{\circ}

4.47mins
Q8b

Determine whether it is possible to draw a triangle given each set of information. Sketch all possible triangles where appropriate. Calculate, then label, all side lengths to the nearest tenth of ta centimetre and all angles to the nearest degree.

a = 11.1 cm, c = 5.2 cm, \angle C = 33^{\circ}

1.11mins
Q8c

Two forest fire stations, P and Q, are 20.0 km apart. A ranger at station Q sees a fire 15.0 km away. If the angle between the line PQ and the line from P to the fire is 25^{\circ}, how far, to the nearest tenth of a kilometre, is station P from the fire?

3.11mins
Q9

Determine each unknown side length to the nearest tenth.

0.32mins
Q10a

Determine each unknown side length to the nearest tenth.

0.24mins
Q10b

Two spotlights, one blue and the other white, are placed 6.0 m apart on a track on the ceiling of a ballroom. A stationary observer standing on the ballroom floor notices that the angle of elevation is 45^{o} to the blue spotlight and 70^{o} to the white one. How high, to the nearest tenth of a metre, is the ceiling of the ballroom?

To determine the height of a pole across a road, Justin takes two measurements. He stands at point A directly across from the base of the pole and determine that the angle of elevation to the top of the pole is 15.3^{o}. He then walks 30 m parallel to the freeway to point C, where he sees that the base of the pole and point A are 57.5^{o} apart. From point A, the base of the pole and point C are 90.0^{o} apart. Calculate the height of the pole to the nearest metre.