2.2 Trig Functions of Non-Acute Angles

Reference Angle

For angle θ, the reference angle θ’, is the positive acute angle made by the terminal side of angle θ and the x-axis.

(label each angle as θ and each reference angle as θ’.)

Find the reference angle for each angle.

a) 294 ^o b) 883 ^o

Summary for Reference angle in terms of 0 ^o < θ < 360^o

(Label each angle θ and each reference angle in terms of θ)

Special Angles as Reference Angles

Find the value of the six trig functions for θ=135 ^o

** Be careful of the sign of each function!!

Finding Trig Function Values for Any NonQuadrantal Angle θ

1. If θ > 360 ^o, or if θ < 0 ^o, then find a co terminal angle by adding or

subtracting 360 ^o as many times as need to get an angle greater than

0 ^o but less than 360 ^o.

2. Find the reference angle θ’.

3. Find the trigonometric function values for reference angle θ’.

4. Determine the correct signs for the values in step 3.

(**Remember: All Students Take Calculus)

Find the exact value of:

Sin (-150 ^o)

cot(780 ^o)

Evaluate:

Evaluate by first expressing the function in terms of an angle between 0 ^{o and} 360 ^o

a) sin 585 ^o

b) cot (-930 ^o )

Finding Angle Measure with Special angles

That is: Given the value of a specific θ, find all possible values for θ.

Find all values of θ, if 0 ^o < θ < 360^o and