7) Use the given figure to write the trigonometric ratio as fractions and as decimals rounded to the nearest hundredth. 8) to a. sinY = d. sinX = Y b. cosY = e. cosX = 15 C. tanY = f. tanX = X 12
7) Use the given figure to write the trigonometric ratio as fractions and as decimals rounded to the nearest hundredth. 8) to a. sinY = d. sinX = Y b. cosY = e. cosX = 15 C. tanY = f. tanX = X 12
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Concept explainers
Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
Question
Use the given figure to write the trigonometric ratio as fractions and as decimals. Round to the nearest hundredth
Transcribed Image Text:**Instructions:**
Use the given figure to write the trigonometric ratios as fractions and as decimals rounded to the nearest hundredth.
**Trigonometric Ratios:**
a. sinY =
b. cosY =
c. tanY =
d. sinX =
e. cosX =
f. tanX =
**Figure Explanation:**
The given figure is a right triangle XYZ, where:
- Angle Y is opposite side XZ.
- Angle X is opposite side YZ.
- Side YZ = 9 (opposite side for angle X, adjacent side for angle Y)
- Side XZ = 12 (adjacent side for angle X, opposite side for angle Y)
- Hypotenuse XY = 15.
**Calculations:**
To find the trigonometric ratios using the sides of the right triangle, we use the definitions of sine (sin), cosine (cos), and tangent (tan):
1. **sinY** (opposite/hypotenuse):
- sinY = YZ / XY = 9 / 15 = 0.60
2. **cosY** (adjacent/hypotenuse):
- cosY = XZ / XY = 12 / 15 = 0.80
3. **tanY** (opposite/adjacent):
- tanY = YZ / XZ = 9 / 12 = 0.75
4. **sinX** (opposite/hypotenuse):
- sinX = XZ / XY = 12 / 15 = 0.80
5. **cosX** (adjacent/hypotenuse):
- cosX = YZ / XY = 9 / 15 = 0.60
6. **tanX** (opposite/adjacent):
- tanX = XZ / YZ = 12 / 9 = 1.33
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