How To Find The Reference Angle In Radians and Degrees - Trigonometry

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Posted on: Apr 24, 2025

Video by: The Organic Chemistry Tutor

This trigonometry video tutorial provides a basic introduction into reference angles. It explains how to find the reference angle in radians and degrees. Trigonometry Final Exam Review: https://www.youtube.com/watch?v=OAsbx4TEnL0 Trigonometry - Free Formula Sheet: https://www.video-tutor.net/formula-sheets.html Trigonometry Video Lessons: https://www.video-tutor.net/basic-trigonometry.html Final Exam and Test Prep Videos: https://bit.ly/41WNmI9

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Video Transcript

0:01

now let's talk about reference angles

0:03

and how to find them

0:06

so let's say if we have an angle

0:09

of 120 degrees

0:12

what is the reference angle

0:15

so let's draw 120 degrees 120

0:18

is in quadrant two

0:23

so this is 120 relative to the positive

0:26

x-axis

0:27

the reference angle

0:29

is the angle between the x-axis

0:33

and the terminal side or the terminal

0:34

array

0:35

and it's always less than 90. it's

0:37

between 0 and 90.

0:39

so what is the angle here

0:43

to find that angle we know it's

0:46

if this angle is 180

0:48

and this is 120 it has to be the

0:50

difference between the two

0:51

so it's 180 minus

0:54

120

0:55

so this angle is 60 and that's the

0:57

reference angle

0:59

so let's try another example what is the

1:01

reference angle

1:03

for an angle that's 210 relative to

1:05

positive x-axis

1:08

so this is 210

1:12

and we know the negative x-axis is 180.

1:14

so the difference is 30.

1:17

so the reference angle is always between

1:19

a terminal ray and the x-axis

1:23

now there are some equations that you

1:25

can use to easily find the reference

1:27

angle

1:29

so anytime you have an angle in quadrant

1:32

one the reference angle

1:34

is equal to the angle in quadrant one

1:38

if you have an angle in quadrant two the

1:40

reference angle

1:42

is going to be 180 minus the angle in

1:45

quadrant two

1:47

if the angle is in quadrant three

1:50

the reference angle

1:51

is going to be the angle in quadrant

1:53

three minus 180

1:56

now if the angle is in quadrant four

1:58

then it's going to be 360 minus the

2:01

angle in quadrant four

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