Precalculus : Trigonometric Functions

Example Questions

Example Question #1 : Find The Degree Measure Of An Angle

Given a triangle, the first angle is three times the value of the second angle.  The third angle is .  What is the value of the second largest angle in degrees?

Explanation:

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

Convert the radians angle to degrees by substituting  for every .

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 .

Solve for .

Substitute  for the first angle and second angle.

The second angle is:

The first angle is:

The three angles are:

The second highest angle is:

Example Question #6 : Angles In The Coordinate Plane

Find the coterminal angle of 15 degrees.

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.

All of these angles are coterminal angles.

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

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

Explanation:

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

These are all coterminal angles to  radians.

Example Question #8 : Angles In The Coordinate Plane

Of the following choices, find a coterminal angle of .

Explanation:

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

The possible angles after subtracting decrements of  radians are:

Out of the given possibilities, only  is a valid answer.

Example Question #9 : Angles In The Coordinate Plane

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

Explanation:

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

For :

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

Example Question #10 : Angles In The Coordinate Plane

Find the coterminal angle of , if possible.

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.

The only correct answer is .

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

Which of the following angles is coterminal to ?

Explanation:

Which of the following angles is coterminal to ?

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,  is coterminal with , 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 . Of the answer choices, only 1 ends in quadrant 1, so that one must be our answer:

Example Question #1 : Convert Between Degrees And Radians

Explanation:

In order to solve this problem, we must know that

with this formula, we can find our answer:

Example Question #1 : Convert Between Degrees And Radians

Explanation:

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

using this formula, we can find our answer:

Example Question #1 : Convert Between Degrees And Radians

Convert   to degrees.