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```NAME ______________________________________________ DATE
9-8
____________ PERIOD _____
Sine, Cosine, and Tangent Ratios
(Pages 477– 481)
Trigonometry is the study of triangle measurement. The ratios of the
measures of the sides of a right triangle are called trigonometric ratios.
Three common trigonometric ratios are defined below.
If ABC is a right triangle and A is an acute angle,
measure of the leg opposite A
measure of the hypotenuse
measure of the leg adjacent to A
cosine of A measure of the hypotenuse
measure of the leg opposite A
tangent of A measure of the leg adjacent to A
Symbols: sin A a, cos A b, tan A a
c
c
b
B
sine of A Definition of
Definition of
Trigonometric
Ratios
c
A
a
C
b
Examples
a. Find sin K to the nearest
thousandth.
measure of leg opposite K
measure of hypotenuse
4
or 0.8
5
5
sin K K
3
M
b. Use a calculator to find the measure
of A given that sin A 0.7071.
4
Enter 0.7071 and the press the sin1 key (you may
have to press INV or 2nd and then the sin key to get
sin1) The calculator should then display 44.999451.
Rounded to the nearest degree, the measure of A
is 45°.
L
Practice
For each triangle, find sin A, cos A, and tan A to the nearest
thousandth.
1. A
2.
3.
30
12
T
16
16
Y
X
20
R
34
M
37
A
A
12
35
N
Use a calculator to find each ratio to the nearest ten thousandth.
4. cos 43°
5. sin 26°
6. sin 36°
7. tan 68°
8. cos 75°
9. tan 29°
Use a calculator to find the angle that corresponds to each ratio.
Round answers to the nearest degree.
10. sin X 0.5
11. sin B 0.669
12. tan K 1.881
13. Sports A skateboarder builds a ramp to perform jumps. If the ramp is
5 feet long and 3 feet high, what angle does it make with the ground?
14. Standardized Test Practice Use a calculator to find sin 56° to the nearest
ten thousandth.
A 0.5600
B 0.8290
C 1.6643
D 88.9770
Answers: 1. 0.8; 0.6; 1.333 2. 0.882; 0.471; 1.875 3. 0.324; 0.946; 0.343 4. 0.7314 5. 0.4384 6. 0.5878 7. 2.4751
8. .2588 9. 0.5543 10. 30° 11. 42° 12. 62° 13. about 31° 14. B