1. 8-2 Trigonometric Ratios Warm Up Lesson Presentation Lesson Quiz
Holt Geometry

2. <C a b
<B c b

3. 7)
x = 7.25

4. Objectives Find the sine, cosine, and tangent of an acute angle.
Use trigonometric ratios to find side lengths in right triangles and to solve real-world problems.

5. SOH-CAH-TOA opposite sin x = hypotenuse opposite tan x = adjacent
cos x =
hypotenuse

6. opposite
Sin(x)=
hypotenuse
ALWAYS an ANGLE!!!

7. In trigonometry, the letter of the vertex of the angle is often used to represent the measure of that angle. For example, the sine of A is written as sin A.
Writing Math

8. Example 1: Finding Trigonometric Ratios
Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.
sin J 60
sin J = 61

9. Example 2: Finding Trigonometric Ratios
Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.
cos J 11
cos J = 61

10. Example 3: Finding Trigonometric Ratios
Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.
tan K 11
tan k = 60

11. Example 4
Write the trigonometric ratio as a fraction and as a decimal rounded to
the nearest hundredth.
cos A 24
cos A = 25

12. s√3 √3 = cos 30 = 2s 2 √3 cos 30 = 2 Example 7:
Write cos 30° as a fraction.
s√3 √3 =
cos 30 = 2s 2 √3
cos 30 = 2

13. Example 8
Use a special right triangle to write tan 45° as a fraction. s
45°
Draw and label a 45º-45º-90º ∆. s
tan 45 = =1 s

14. Example 9
Use your calculator to find the trigonometric ratio. Round to the nearest hundredth.
sin 52°
Be sure your calculator is in degree mode, not radian mode.
Caution!
sin 52°  0.79

15. Example 10
Use your calculator to find the trigonometric ratio. Round to the nearest hundredth.
cos 19°
cos 19°  0.95

17. S O H C A H T O A hyp opp x adj The trigonometric functions are:
sine, cosine, tangent, cotangent, secant, and cosecant.
sin x = cos x = tan x =
csc x = sec x = cot x =
hyp
adj
opp
hyp
hyp
adj
opp
adj
opp
S O H C A H T O A

18. S O H C A H T O A 13 5 x 12 Find the following:
sine, cosine, tangent, cotangent, secant, and cosecant. 5 12 5
sin x = cos x = tan x =
csc x = sec x = cot x = 13 13 12 13 13 12 5 12 5
S O H C A H T O A

19. S O H C A H T O A x 5 3 4 Find the following:
sine, cosine, tangent, cotangent, secant, and cosecant. 4 3 4
sin x = cos x = tan x =
csc x = sec x = cot x = 5 5 3 5 5 3 4 3 4
S O H C A H T O A

20. Opposite
Adjacent
So… the hypotenuse = 5 3 4
sin x = cos x = tan x =
csc x = sec x = cot x = 3 5 4 5 5 3 5 4 4 3

21. Caution!
Do not round until the final step of your answer. Use the values of the trigonometric ratios provided by your calculator.

22. Example 14
Find the length. Round to the nearest hundredth.
opp
adj BC
BC  ft

23. Example 4B:
Find the length. Round to the nearest hundredth.
opp QR
hyp
12.9(sin 63°) = QR
11.49 cm  QR

24. Example 4C
Find the length. Round to the nearest hundredth.
hyp FD
adj
FD  m