Given a right triangle, what is the measure of angle if is the smallest angle and the other two angles are and ?
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- 0. Review of College Algebra4h 45m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
2. Trigonometric Functions on Right Triangles
Trigonometric Functions on Right Triangles
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Which of the following is the correct definition of the sine function for an acute angle in a right triangle?
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Recall that in a right triangle, the sine of an acute angle \( \theta \) is defined as the ratio of the length of the side opposite to \( \theta \) to the length of the hypotenuse.
Identify the three sides relative to the angle \( \theta \): the opposite side (across from \( \theta \)), the adjacent side (next to \( \theta \)), and the hypotenuse (the longest side opposite the right angle).
Write the sine function as \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \).
Compare this definition with the given options to determine which fraction matches the sine function's definition.
Conclude that the correct definition of sine for an acute angle \( \theta \) in a right triangle is \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \).
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