Given a right triangle where the side adjacent to angle is units and the hypotenuse is units, what is the value of ?
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
In a right triangle, which of the following ratios represents the cosine of angle ?
A
B
C
D
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Verified step by step guidance1
Recall the definition of cosine in a right triangle: cosine of an angle \( \theta \) is the ratio of the length of the side adjacent to \( \theta \) to the length of the hypotenuse.
Identify the sides of the triangle relative to angle \( \theta \): the 'adjacent' side is the one next to \( \theta \) (but not the hypotenuse), the 'opposite' side is across from \( \theta \), and the 'hypotenuse' is the longest side opposite the right angle.
Write the cosine ratio as \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \).
Compare this ratio to the given options to determine which one matches the cosine definition.
Conclude that the ratio representing cosine of angle \( \theta \) is the one with 'adjacent' over 'hypotenuse'.
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