In a right triangle, what is the longest side called?
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 of the following correctly expresses the sine of angle in a right triangle in terms of the lengths of the sides?
A
B
C
D
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Verified step by step guidance1
Recall the definition of sine in a right triangle: sine of an angle \( \theta \) is the ratio of the length of the side opposite to \( \theta \) to the length of the hypotenuse.
Write the sine function using the sides of the triangle: \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \).
Understand that the adjacent side is not part of the sine ratio; it is used in the cosine ratio instead.
Compare the given options to the definition and identify which fraction matches \( \frac{\text{opposite}}{\text{hypotenuse}} \).
Conclude that the correct expression for \( \sin(\theta) \) is the one where sine equals the opposite side over the hypotenuse.
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