Given the right triangle below, evaluate .
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
Given the right triangle below, use the cosine function to write a trigonometric expression for the missing angle ϕ.

A
ϕ=cos−1(1312)
B
ϕ=cos−1(513)
C
ϕ=cos−1(1213)
D
ϕ=cos−1(135)
0 Comments
Verified step by step guidance1
Identify the sides of the right triangle: the hypotenuse is 13, the adjacent side to angle ϕ is 12, and the opposite side to angle ϕ is 5.
Recall the definition of the cosine function in a right triangle: \( \cos(\phi) = \frac{\text{adjacent}}{\text{hypotenuse}} \).
Substitute the known values into the cosine function: \( \cos(\phi) = \frac{12}{13} \).
To find the angle ϕ, use the inverse cosine function: \( \phi = \cos^{-1}\left(\frac{12}{13}\right) \).
Compare the given options to find the correct expression for angle ϕ. The correct expression is \( \phi = \cos^{-1}\left(\frac{5}{13}\right) \), which matches the given correct answer.
Related Videos
Related Practice
Multiple Choice

