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AssignmentMultiple Select

Trigonometric Difference Identities

Question 1 • Precalculus

Which statements involving cosine and sine are true? Check all that apply. sin(–45°) = –sin(45°)sin(–45°) = sin(45°)cos(–45°) = –cos(45°)cos(–45°) = cos(45°)cos(–45°) = sin(–45°)

Answer
A
sin(–45°) = –sin(45°)
B
sin(–45°) = sin(45°)
C
cos(–45°) = –cos(45°)
D
cos(–45°) = cos(45°)
E
cos(–45°) = sin(–45°)

Explanation

Sine is an odd function, so sin(−θ) = −sin(θ); therefore sin(−45°) = −sin(45°), making A true. Cosine is an even function, so cos(−θ) = cos(θ); therefore D is true. Since sin(45°) is positive and cos(45°) is positive, B and C are false, and cosine and sine at −45° are not equal, so E is false.

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