Trigonometry Chapter Review
Chapter
Chapter 4
Section
Trigonometry Chapter Review
Purchase this Material for $10
You need to sign up or log in to purchase.
Subscribe for All Access
You need to sign up or log in to purchase.
Solutions 41 Videos

Determine the approximate radian measure, to the nearest hundredth.

\displaystyle 33^o

Buy to View
0.22mins
Q1a

Determine the approximate radian measure, to the nearest hundredth.

\displaystyle 138^o

Buy to View
0.29mins
Q1b

Determine the approximate radian measure, to the nearest hundredth.

\displaystyle 252^o

Buy to View
0.34mins
Q1c

Determine the approximate radian measure, to the nearest hundredth.

\displaystyle 347^o

Buy to View
0.28mins
Q1d

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

1.24

Buy to View
0.26mins
Q2a

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

2.82

Buy to View
0.29mins
Q2b

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

4.78

Buy to View
0.15mins
Q2c

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

6.91

Buy to View
0.17mins
Q2d

Determine the exact radian measure.

\displaystyle 75^o

Buy to View
0.19mins
Q3a

Determine the exact radian measure.

\displaystyle 20^o

Buy to View
0.20mins
Q3b

Determine the exact radian measure.

\displaystyle 12^o

Buy to View
0.21mins
Q3c

Determine the exact radian measure.

\displaystyle 9^o

Buy to View
0.15mins
Q3d

Determine the exact degree measure of each angle.

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

Buy to View
0.13mins
Q4a

Determine the exact degree measure of each angle.

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

Buy to View
0.11mins
Q4b

Determine the exact degree measure of each angle.

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

Buy to View
0.27mins
Q4c

Determine the exact degree measure of each angle.

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

Buy to View
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

b) radians per second

Buy to View
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
Buy to View
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

  • radians per second
Buy to View
1.16mins
Q6b

Determine an exact value for each expression.

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

Buy to View
0.29mins
Q8a

Determine an exact value for each expression.

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

Buy to View
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.

Buy to View
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.

Buy to View
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.

Buy to View
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}

Buy to View
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}

Buy to View
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.

Buy to View
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}

Buy to View
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}

Buy to View
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}

Buy to View
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}

Buy to View
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.
Buy to View
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.
Buy to View
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).
Buy to View
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.

Buy to View
2.01mins
Q16

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

Buy to View
1.25mins
Q17

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

Buy to View
0.25mins
Q18

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

Buy to View
1.31mins
Q19a

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

Buy to View
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.

Buy to View
0.30mins
Q22

Prove that \displaystyle (\sin 2x)(\tan x + \cot x) =2

Buy to View
0.38mins
Q23