In a right triangle
Table of contents
- 0. Review of College Algebra4h 43m
- 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
- OLD 1. Angles and the Trigonometric Functions Coming soon
- OLD 2. Trigonometric Functions graphs, Inverse Trigonometric Functions Coming soon
- OLD 3. Trigonometric Identities and Equations Coming soon
- OLD 4. Laws of Sines, Cosines and Vectors Coming soon
- OLD 5. Complex Numbers, Polar Coordinates and Parametric Equations Coming soon
- NEW (not used) 7. Laws of Sines, Cosines and Vectors Coming soon
- NEW (not used) 8. Vectors Coming soon
- NEW(not used) 9. Polar equations Coming soon
- NEW (not used) 11. Graphing Complex Numbers Coming soon
2. Trigonometric Functions on Right Triangles
Trigonometric Functions on Right Triangles
Multiple Choice
Which equation correctly relates the measure of angle in a right triangle to the lengths of the opposite side and the hypotenuse ?
A
B
C
D
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Verified step by step guidance1
Recall the definitions of the primary trigonometric ratios in a right triangle: sine, cosine, and tangent. These relate an angle to ratios of specific sides.
Identify the sides relative to the angle \( \theta_1 \): the opposite side (O) is the side opposite to \( \theta_1 \), the adjacent side is next to \( \theta_1 \), and the hypotenuse (H) is the longest side opposite the right angle.
The sine of an angle is defined as the ratio of the length of the opposite side to the hypotenuse, expressed as \( \sin(\theta_1) = \frac{O}{H} \).
The cosine of an angle is the ratio of the adjacent side to the hypotenuse, \( \cos(\theta_1) = \frac{\text{Adjacent}}{H} \), and the tangent is the ratio of the opposite side to the adjacent side, \( \tan(\theta_1) = \frac{O}{\text{Adjacent}} \).
Compare the given options to these definitions to determine which equation correctly relates \( \theta_1 \) to the sides O and H. The correct equation matches the sine definition: \( \sin(\theta_1) = \frac{O}{H} \).
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