Download Math 1316 Section 2.2 Class Notes Trigonometric Functions of Non

Math 1316
Trigonometric Functions of Non-Acute Angles
Section 2.2 Class Notes
Reference Angles
To find the reference angle of an angle, first find its coterminal angle then sketch the standard position
angle to find the reference angle.
Caution: A common error is to find the reference angle by using the terminal side of θ and the y-axis.
The reference angles is always found with reference to the x-axis.
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Math 1316
Section 2.2 Class Notes
Example 1: Find the reference angle for each angle.
a. 2180
b. 13870
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Math 1316
Section 2.2 Class Notes
Finding Trigonometric Function Values Using Reference Angles
A Technique for Using Reference Angles to Evaluate Trigonometric Functions:
Example 2:
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Math 1316
Section 2.2 Class Notes
Example 3: Find exact values of the six trigonometric functions for each angle using reference angle.
1. 3000
2. 4200
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Math 1316
Section 2.2 Class Notes
3. 15000
4. -8550
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Math 1316
Section 2.2 Class Notes
Example 4: Find exact values of expressions.
1. sin 13050
2. tan(-10200)
Example 5: Determine whether each statement is true or false. If false, tell why.
1. cos 600 = 2cos 300
2. sin 1200 = sin 1500 – sin 300
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Math 1316
Section 2.2 Class Notes
Example 6: Without using a calculator, find all values of θ, if θ is in the interval [0, 3600) and has the
given function value.
1. cos  
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2
2. cot   
3
3
3. sec    2
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