Use a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. cos 40° = 2 cos 20°
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
6. Trigonometric Identities and More Equations
Introduction to Trigonometric Identities
Multiple Choice
Select the expression with the same value as the given expression.
sin(−38°)
A
sin38°
B
−sin38°
C
−sin(−38°)
D
−sin38°1
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Verified step by step guidance1
Understand the property of the sine function: \( \sin(-x) = -\sin(x) \). This property states that the sine of a negative angle is the negative of the sine of the positive angle.
Apply the property to the given expression \( \sin(-38\degree) \). Using the property, we can rewrite this as \( -\sin(38\degree) \).
Compare the rewritten expression \( -\sin(38\degree) \) with the options provided.
Identify that \( -\sin(38\degree) \) matches one of the options given, which is \( -\sin(38\degree) \).
Conclude that the expression \( \sin(-38\degree) \) is equivalent to \( -\sin(38\degree) \) based on the trigonometric identity.
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