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Warm Up
5.3 part 2 – Finding Reference
Angles
Fill in the following table:
x
Sin x
Cos x
Tan x
Csc x
Sec x
Cot x
30°
Objective: TSW apply the cofunction
identities and find reference angles.
45°
60°
Cofunction Identities - two acute angles in a
right triangle show that sin A=cos B and
sin B = cos A, therefore the following are true:
sin A = cos(90 0 − A)
csc A = sec(900 − A)
cos A = sin(90 0 − A)
sec A = csc(900 − A)
tan A = cot(90 0 − A)
cot A = tan(900 − A)
Examples: Write each function in
terms of its cofunction.
1. sin 9°
2. cot 76°
3. csc 45°
Reference Angles: written as ө’
1. Positive ACUTE angle (always less than 90°
2. ALWAYS relate to the x-axis
3. If ө is your angle, then ө’ is the reference
angle
Let’s look at what a reference angle
looks like in each quadrant.
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
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Examples
4. Find the reference angle for 294°
Example 6
Find the reference angle for 926°
5. Find the reference angle for -192°
Finding exact values for trig functions
using reference angles.
7. Find the values of sin,cos,tan for 135°.
Example 9
Find the exact value of cot(780°)
Example 8
Find the exact value of sin(–150°)
Using Inverse Trig Functions to Find
Angle Measures
WHEN WE ARE TRYING TO FIND AN UNKNOWN
ANGLE!
You use the sin-1, cos-1 , tan-1 ONLY when you are
finding angle measures!!!
Also known as arcsin, arccos, arctan
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Examples: Use a calculator to find an angle θ in the interval
[0°, 90°] that satisfies each condition.
11.
Homework Time
5.3 part 2 page 525 #’s 17-23 odd,57-63 odd,
64-71 all, 73,75,113-129 odd
ALSO, FILL IN ALL COORDINATES OF YOUR UNIT
CIRCLE
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