Trigonometry Chapter Review
Chapter
Chapter 4
Section
Trigonometry Chapter Review
Solutions 41 Videos

Determine the approximate radian measure, to the nearest hundredth.

 \displaystyle 33^o 

0.22mins
Q1a

Determine the approximate radian measure, to the nearest hundredth.

 \displaystyle 138^o 

0.29mins
Q1b

Determine the approximate radian measure, to the nearest hundredth.

 \displaystyle 252^o 

0.34mins
Q1c

Determine the approximate radian measure, to the nearest hundredth.

 \displaystyle 347^o 

0.28mins
Q1d

Determine the approximate degree measure, to the nearest tenth, for each angle.

1.24

0.26mins
Q2a

Determine the approximate degree measure, to the nearest tenth, for each angle.

2.82

0.29mins
Q2b

Determine the approximate degree measure, to the nearest tenth, for each angle.

4.78

0.15mins
Q2c

Determine the approximate degree measure, to the nearest tenth, for each angle.

6.91

0.17mins
Q2d

 \displaystyle 75^o 

0.19mins
Q3a

 \displaystyle 20^o 

0.20mins
Q3b

 \displaystyle 12^o 

0.21mins
Q3c

 \displaystyle 9^o 

0.15mins
Q3d

Determine the exact degree measure of each angle.

 \displaystyle \frac{2\pi}{5} 

0.13mins
Q4a

Determine the exact degree measure of each angle.

 \displaystyle \frac{4\pi}{9} 

0.11mins
Q4b

Determine the exact degree measure of each angle.

 \displaystyle \frac{7\pi}{12} 

0.27mins
Q4c

Determine the exact degree measure of each angle.

 \displaystyle \frac{11\pi}{18} 

0.13mins
Q4d

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

1.18mins
Q5

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
1.07mins
Q6a

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

1.16mins
Q6b

Determine an exact value for each expression.

 \displaystyle \frac{\cot\frac{\pi}{4}}{\cos\frac{\pi}{3}\csc \frac{\pi}{2}} 

0.29mins
Q8a

Determine an exact value for each expression.

 \displaystyle \cos \frac{\pi}{6} \csc \frac{\pi}{3} + \sin \frac{\pi}{4} 

0.28mins
Q8b

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.

1.06mins
Q9

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.

0.46mins
Q10

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.

1.00mins
Q11

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} 

1.07mins
Q12a

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} 

0.33mins
Q12b

Given that \tan \sin x = \cos \frac{3\pi}{11} and that x lies in the second quadrant, determine the measure of angle x.

0.55mins
Q13

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} 

0.36mins
Q14a

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} 

0.25mins
Q14b

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} 

0.35mins
Q14c

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} 

0.33mins
Q14d

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.
0.22mins
Q15a

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.
0.39mins
Q15b

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).
0.54mins
Q15c

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.

2.01mins
Q16

Determine an exact value for \cos \frac{13\pi}{12}

1.25mins
Q17

Prove that  \displaystyle \sin(2\pi -x ) = -\sin x 

0.25mins
Q18

Prove that  \displaystyle \sec x = \frac{2(\cos x \sin 2x - \sin x \cos 2x)}{\sin 2x} 

1.31mins
Q19a

Prove that  \displaystyle 2\sin x \cos y = \sin(x + y) + \sin(x - y) 

0.30mins
Q20

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