Download section 2.1 Trigonometric Functions of Acute Angles.jnt

Math 1316
Section 2.1 Class Notes
Trigonometric Functions of Acute Angles
Right-Triangle-Based Definition of Trigonometric Functions
Note that if θ is an acute angle in standard position and we draw a right triangle as shown in the figure
below, then the definition of the six trigonometric functions of θ agree with the previous definition of
the six trigonometric ratios given above.
Example 1: Find exact values for sin A, cos A, and tan A.
B
53
A
45
28
28
C
1
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Math 1316
Section 2.1 Class Notes
0
0
Example 2: Find exact value of each expression using the 30 -60 right triangle and isosceles right
triangle.
1. cot 300
300
2. cos 600
3. sec 450
450
4. sin 450
2
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Math 1316
Section 2.1 Class Notes
Example 2: Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find
the unknown side length using Pythagorean Theorem, and find the exact values of the six trigonometric
functions for angle B.
1. a = 3, b = 5
2. b = 8, c = 11
3
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Math 1316
Section 2.1 Class Notes
Example 3: Write each function in terms of its cofunction. Assume that all unknown appears are acute
angles.
1. cot 730
2. cos(α + 200)
Example 4: Find one solution for each equation. Assume that all angles in which an unknown appears
are acute angles.
1. cos θ = sin 2 θ
2. cot(5θ + 20) = tan(2θ + 40)
4
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Math 1316
Section 2.1 Class Notes
Trigonometric Function Values of Special Angles
Example: Use the table to find:
1. tan 450
2. sin 300
3. csc600
Example: Use calculator to find the approximation to 2 decimal places of the following functions.
1. sin 40o
2. cos 172o
3. sec (-38o)
5
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Math 1316
Section 2.1 Class Notes
4. csc(3908o)
5. tan 71o
6. sin 60o
Example: Find the exact value of each part labeled with a variable in each figure.
6
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