Evaluate trigonometric functions

1
EXAMPLE 1
Evaluate trigonometric functions
SOLUTION
2
EXAMPLE 1
Evaluate trigonometric functions
3
EXAMPLE 2
Standardized Test Practice
SOLUTION
STEP 1
4
EXAMPLE 2
Standardized Test Practice
STEP 2
Find the value of tan ?.
5
EXAMPLE 3
Find an unknown side length of a right triangle
SOLUTION
Write an equation using a trigonometric function
that involves the ratio of x and 8. Solve the
equation for x.
Write trigonometric equation.
Substitute.
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EXAMPLE 3
Find an unknown side length of a right triangle
Multiply each side by 8.
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EXAMPLE 4
Use a calculator to solve a right triangle
SOLUTION
68º.
Write trigonometric equation.
Substitute.
8
EXAMPLE 4
Use a calculator to solve a right triangle
Solve for the variable.
15(tan 28º) a
Use a calculator.
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EXAMPLE 5
Use indirect measurement
Grand Canyon
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EXAMPLE 5
Use indirect measurement
SOLUTION
Write trigonometric equation.
2(tan 76º) x
Multiply each side by 2.
Use a calculator.
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EXAMPLE 6
Use an angle of elevation
Parasailing
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EXAMPLE 6
Use an angle of elevation
SOLUTION
STEP 1
Draw a diagram that represents the situation.
STEP 2
Write and solve an equation to find the height h.
Write trigonometric equation.
300(sin 48º) h
Multiply each side by 300.
Use a calculator.
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EXAMPLE 1
Draw angles in standard position
Draw an angle with the given measure in standard
position.
a. 240º
SOLUTION
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EXAMPLE 1
Draw angles in standard position
Draw an angle with the given measure in standard
position.
b. 500º
SOLUTION
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EXAMPLE 1
Draw angles in standard position
Draw an angle with the given measure in standard
position.
c. 50º
SOLUTION
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EXAMPLE 2
Find coterminal angles
Find one positive angle and one negative angle
that are coterminal with (a) 45º and (b) 395º.
SOLUTION
a. 45º 360º
315º
45º 360º
405º
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EXAMPLE 2
Find coterminal angles
b. 395º 360º
35º
395º 2(360º)
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EXAMPLE 3
Convert between degrees and radians
a. 125º
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EXAMPLE 4
Solve a multi-step problem
Softball
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EXAMPLE 4
Solve a multi-step problem
SOLUTION
STEP 1
Convert the measure of the central angle to
radians.
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EXAMPLE 4
Solve a multi-step problem
STEP 2
Find the arc length and the area of the sector.