Which of the following statements best describes the relationship between the acute angles in a right triangle according to the linear pair perpendicular theorem?
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 a right triangle, which of the following is equal to ?
A
B
C
D
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Verified step by step guidance1
Recall that in a right triangle, the two non-right angles are complementary, meaning their measures add up to 90°. So, if one angle is 38°, the other must be 90° - 38° = 52°.
Understand the relationship between sine and cosine for complementary angles: \(\sin(\theta) = \cos(90^\circ - \theta)\).
Apply this identity to the given angle: \(\sin(38^\circ) = \cos(90^\circ - 38^\circ) = \cos(52^\circ)\).
Recognize that this means \(\sin(38^\circ)\) is equal to \(\cos(52^\circ)\), which matches one of the given options.
Note that tangent functions do not directly equal sine of an angle unless related through other identities, so the correct choice is the cosine of the complementary angle.
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