Unit Circles & Reference Angles

Unit Circle- Is used for

• 0 degrees
• 90 degrees
• 180 degrees
• 270 degrees
• 360 degrees
• 0
• pie/2
• pie
• 3pie/2
• 2pie

-The angle tells you which point to use in the formulas

Sin Theta = y/r

Cos Theta = x/r

Tan Theta = y/x

Csc Theta = r/y

Sec Theta = r/x

Cot Theta = x/y

Examples 1: If Theta is a 4th quadrant angle and Sin Theta = 5/13. Find Cos Theta

Draw a triangle in the 4th quadrant with the y leg as 5 and the hypotenuse as 13

To find the other side you have to use the Pythagorean Theorem 

13^2 = x^2 + 5^2

169 = x&2 +25

144 = x^2

x=12

Cos Theta = 12/13

Step1) Draw triangle and label given legs

Step2) Find the missing leg

Step3) Plug into Cos (x/r)

Reference Angles

Reference Angles are like reduced fractions. They must be between 0 degrees and 90 degrees.

Steps:

1. Find the original quadrant and sketch
2. Determine if the angle is positive or negative using unit circle method
3. Subtract 360 degrees or 180 degrees until the absolute value of theta is between 0 degrees and 90 degrees

Example 1: Express Sin 695 degrees = -Sin25 degrees

Step1) Sketch and Find quadrant

Step2) determine if + or -

Step3) Subtract 360 from 695 TWICE