This is a free lesson from our course in Trigonometry
This lesson introduce to the key concepts of reference angle and how to find the reference angle to a
given angle. You'll learn with the help of several examples and explanation by instructor
using video, how to deal with problems that involve angular measures and how to
calculate the exact values of trigonometric functions for any angle using reference
angles and then determining its sign, depending on the quadrant.
The reference angle is defined as the acute angle between the terminal side of the given angle
and the x axis. The given angle may be in degrees or radians.
(More text below video...)
In the Second quadrant: Only sine and cosec functions are positive.
In the third quadrant: Only tangent and cotangent functions are positive.
In the fourth quadrant: Only cosine and secant functions are positive.
The reference angles for different quadrants are as follows:
Angle (90 
) lies in first
quadrant
Angle (180 
) lies in second
quadrant
Angle (
 180) lies in third quadrant
Angle (360 
) lies in fourth quadrant
For example, the reference angle to angle A = 120
is given by (180
 120) = 60 and
to angle A = 330(that
lies in the IV quadrant), the reference angle is (360
 330) = 30.
The value of sin 30
= 1/2, which gives sin 330
= 1/2.
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