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Precalculus : Trigonometric Functions

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Example Questions

Example Question #1 : Angles In The Coordinate Plane

Given a triangle, the first angle is three times the value of the second angle. The third angle is $\frac{\pi}{3} \textup{ radians}$ . What is the value of the second largest angle in degrees?

Possible Answers:

120

Correct answer:

Explanation:

A triangle has three angles that will add up to 180 degrees.

Convert the radians angle to degrees by substituting $180 \textup{ degrees}$ for every $\pi \textup{ radian}$ .

$\frac{180}{3} = 60 \textup{ degrees}$

The third angle is 60 degrees.

Let the second angle be . The first angle three times the value of the second angle is . Set up an equation that sums the three angles to $180 \textup{ degrees}$ .

3x+x+60 = 180

Solve for .

4x+60 = 180

4x=120

x=30

Substitute x=30 for the first angle and second angle.

The second angle is: x=30

The first angle is: 3x= 3(30) = 90

The three angles are: 30,60,90

The second highest angle is:

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Example Question #1 : Find The Measure Of A Coterminal Angle

Find the coterminal angle of 15 degrees.

Possible Answers:

$\textup{All of the answers represent coterminal angles.}$

$735^{\circ}$

$-345^{\circ}$

$-705^{\circ}$

$375^{\circ}$

Correct answer:

$\textup{All of the answers represent coterminal angles.}$

Explanation:

The coterminal angles can be positive or negative. To find the coterminal angles, simply add or subtract 360 degrees as many times as needed from the reference angle.

15+360=375

15+360+360= 735

15-360=-345

15-360-360=-705

All of these angles are coterminal angles.

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Example Question #1 : Angles In The Coordinate Plane

Of the given answers, what of the following is a coterminal angle of $\pi$ radians?

Possible Answers:

$3\pi$

$-2\pi$

$2\pi$

$\frac{\pi}{2}$

$\frac{3\pi}{2}$

Correct answer:

$3\pi$

Explanation:

To find the coterminal angle of an angle, simply add or subtract $2\pi$ radians, or 360 degrees as many times as needed.

$\pi+2\pi=3\pi$

$\pi-2\pi=-\pi$

$3\pi+2\pi=5\pi$

$-\pi-2\pi=-3\pi$

These are all coterminal angles to $\pi$ radians.

Out of the given answers, $3\pi$ is the only possible answer.

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Example Question #1 : Find The Measure Of A Coterminal Angle

Of the following choices, find a coterminal angle of $\pi$ .

Possible Answers:

$\frac{3}{2}\pi$

$-2\pi$

$6\pi$

$-5\pi$

Correct answer:

$-5\pi$

Explanation:

In order to find a coterminal angle, simply add or subtract $2\pi$ radians to the given angle as many times as possible.

$\theta=\pi+2\pi k$

The possible angles after adding increments of $2\pi$ radians are:

$\pi, 3\pi,5\pi,7\pi...$

$\theta=\pi-2\pi k$

The possible angles after subtracting decrements of $2\pi$ radians are:

$\pi,-\pi,-3\pi,-5\pi...$

Out of the given possibilities, only $-5\pi$ is a valid answer.

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Example Question #1 : Find The Measure Of A Coterminal Angle

Find the coterminal angle of 15 degrees in standard position from the following answers.

Possible Answers:

$365^{\circ}$

$30^{\circ}$

$360^{\circ}$

$-705^{\circ}$

$-1060^{\circ}$

Correct answer:

$-705^{\circ}$

Explanation:

To determine the coterminal angle, simply add or subtract increments or decrements of 360 degrees to the given angle.

For n=1,2,3,... :

15+360n= 375,735,1095...

15-360n= -345,-705,-1065...

These angles can all be coterminal to 15 degrees. The only answer is .

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Example Question #301 : Pre Calculus

Find the coterminal angle of $10^\circ$ , if possible.

Possible Answers:

$\textup{The coterminal angle does not exist.}$

$-190^\circ$

$350^\circ$

$-350^\circ$

$190^\circ$

Correct answer:

$-350^\circ$

Explanation:

In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.

10+360=370

10-360=-350

The only correct answer is .

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Example Question #6 : Find The Measure Of A Coterminal Angle

Which of the following angles is coterminal to $65^{\circ}$ ?

Possible Answers:

$-65^{\circ}$

$-425^{\circ}$

$295^{\circ}$

$-295^{\circ}$

Correct answer:

$-295^{\circ}$

Explanation:

Which of the following angles is coterminal to $65^{\circ}$ ?

Coterminal angles are angles which start and end at the same point. In other words, they share both their starting and ending point. Note, this doesn't require them to be the same angle.

For instance, $120^{\circ}$ is coterminal with $-240^{\circ}$ , because they both start on the positive x-axis, and end at the same place in quadrant 2.

So, we want to find an angle that ends at the same place in quadrant 1 as $65^{\circ}$ . Of the answer choices, only 1 ends in quadrant 1, so that one must be our answer: $-295^{\circ}$

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Example Question #301 : Pre Calculus

Convert $240^{\circ}$ to radians.

Possible Answers:

$\frac{3}{4}\pi$

$\frac{4}{3}\pi$

$\frac{43200}{\pi }$

$\frac{4}{3}$

Correct answer:

$\frac{4}{3}\pi$

Explanation:

In order to solve this problem, we must know that

$\text{Radians}=(\frac{\pi }{180^{\circ}})\times \text{Degrees}$

with this formula, we can find our answer:

$(\frac{\pi }{180^{\circ}}) \times 240^{\circ}=\frac{4}{3}\pi$

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Example Question #1 : Angle Measures In Degrees And Radians

Convert $330^{\circ}$ to radians.

Possible Answers:

$\frac{6}{11}\pi$

$\frac{11}{6}$

$\frac{11}{6}\pi$

$\frac{59400}{\pi }$

Correct answer:

$\frac{11}{6}\pi$

Explanation:

In order to solve this problem, we need to know that

$\text{Radians}=(\frac{\pi }{180^{\circ}})\times \text{Degrees}$

using this formula, we can find our answer:

$(\frac{\pi }{180^{\circ}})\times330^{\circ}= \frac{11}{6}\pi$

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Example Question #2 : Angle Measures In Degrees And Radians

Convert $\frac{5}{6}\pi$ to degrees.

Possible Answers:

$\frac{\pi }{216}$

$150^{\circ}$

$150\pi$

$216^{\circ}$

Correct answer:

$150^{\circ}$

Explanation:

In order to solve this problem, we need to know that

$\text{Degrees}=(\frac{180^{\circ}}{\pi })\times \text{Radians}$

using this formula, we can find our answer:

$(\frac{180^{\circ}}{\pi }) \times \frac{5\pi }{6}= 150^{\circ}$

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Precalculus : Trigonometric Functions

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Angles In The Coordinate Plane

Example Question #1 : Find The Measure Of A Coterminal Angle

Example Question #1 : Angles In The Coordinate Plane

Example Question #1 : Find The Measure Of A Coterminal Angle

Example Question #1 : Find The Measure Of A Coterminal Angle

Example Question #301 : Pre Calculus

Example Question #6 : Find The Measure Of A Coterminal Angle

Example Question #301 : Pre Calculus

Example Question #1 : Angle Measures In Degrees And Radians

Example Question #2 : Angle Measures In Degrees And Radians

All Precalculus Resources

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