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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
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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Use the given figure to write the trigonometric ratio as fractions and as decimals. Round to the nearest hundredth
**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
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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