alleryStart learning →For the same angle with tan x = -3/4 in quadrant II, what is cos(2x)?
A-7 / 25
B-24 / 25
C7 / 25
D24 / 25
Answer & Solution
Correct answer: C. 7 / 25
1. From the reference triangle, sin x = 3/5 and cos x = -4/5.
2. Apply cos(2x) = cos^2 x - sin^2 x.
3. The first square is (-4/5)^2 = 16/25.
4. The second square is (3/5)^2 = 9/25.
5. Subtracting gives 16/25 - 9/25 = 7/25.
6. The result is positive because squaring removes the sign the second quadrant put on the cosine.
7. Choosing -7/25 amounts to computing sin^2 x - cos^2 x, which reverses the order of subtraction.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.3 Double-Angle, Half-Angle, and Reduction Formulas_
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