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4.3 Right Triangle Trigonometry. Students will evaluate trigonometric functions of acute angles. Students will use the fundamental trigonometric identities. Students will use a calculator to evaluate trigonometric functions. - PowerPoint PPT Presentation
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4.3 Right Triangle Trigonometry
• Students will evaluate trigonometric functions of acute angles.
• Students will use the fundamental trigonometric identities.
• Students will use a calculator to evaluate trigonometric functions.
• Students will use trigonometric functions to model and solve real-life problems.
SOHCAHTOA
p. 274 #9
Sketch a right triangle corresponding to the trigonometric function of the acute angle .
sin 5
6
p. 274 #16
Sketch a right triangle corresponding to the trigonometric function of the acute angle .
sin 3
8
p. 274 #17
Construct an appropriate triangle to complete the table.
Function (deg) (rad) Function Value
sin 30 _____ _______
0 90 02
,
x
y (0, 1)
90°2
(–1, 0)
180°
(0, –1)
270°32
360°2 (1, 0)0° 0
Trigonometric Values of Common Angles
60° 3
31 ,2 2
45°4
2 2,2 2
30° 6
3 1,2 2
330°116
3 1,2 2
315°74
2 2,2 2
300°53
31 ,2 2
23
120°
31 ,2 2
34
135°
2 2,2 2
56
150°
3 1,2 2
210°76
3 1,2 2
225°5
4
2 2,2 2
240°43
31 ,2 2
p. 275 #22
Construct an appropriate triangle to complete the table.
Function (deg) (rad) Function Value
csc ______ _____
0 90 02
,
2
p. 275 #29
Use the given function values to find the indicated trigonometric functions.
a.
b.
c.
d.
csc 3 sec 3 2
4sin
cos
tan
sec( )90
Section 4.3, Fundamental Trigonometric Identities, pg. 270
Use the trigonometric identities to transform one side of the equation into the other.
p. 275 #33
02
tan cot 1
Use the trigonometric identities to transform one side of the equation into the other.
p. 275 #35
02
tan cos sin
Use the trigonometric identities to transform one side of the equation into the other.
p. 275 #37
02
( cos )( cos )1 1 1
Use the trigonometric identities to transform one side of the equation into the other.
p. 275 #39
02
sin
cos
cos
sincsc sec
Use a calculator to evaluate the trigonometric function. Round to four decimal places.
p. 275 #43
a. b.sec '42 12 csc '48 7
Find each value in degrees and radians by using your unit circle.
p. 275 #47
a. b.sin 1
2csc 2
02
0 90
p.276 #57A six-foot person walks from the base of a streetlight directly toward the
tip of the shadow cast by the streetlight. When the person is 16 feet from the streetlight and 5 feet from the tip of the streetlight’s shadow, the person’s shadow starts to appear beyond the streetlight’s shadow.
a) Draw a right triangle that gives a visual representation of the problem. Show the known quantities of the triangle and use a variable to indicate the height of the streetlight.
b) Use a trigonometric function to write an equation involving the unknown quantity.
c) What is the height of the streetlight?
:
