3 years ago

Amber is solving this problem. 252 × 605.

Mathematics

2 answers:

expeople1 [14]3 years ago

6 0

The answer would be A

babunello [35]3 years ago

3 0

The answer while be a

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If cos x=8/17, and 270° < x < 360° what is cos(2x)?

svp [43]

Answer: $\bold{-\dfrac{161}{289}}$

Step-by-step explanation:

Given: cos x = $\dfrac{8}{17}$ , x is in Quadrant 4

Use Pythagorean Theorem to find sin x:

8² + y² = 17²

y² = 17² - 8²

y² = 289 - 64

y² = 225

y = 15

→ sin x = $-\dfrac{15}{17}$

Use the double angle formula to find cos (2x):

$cos (2x) = cos^2 x - sin^2 x\\\\.\qquad=\bigg(\dfrac{8}{17}\bigg)^2-\bigg(-\dfrac{15}{17}\bigg)^2\\\\\\.\qquad=\dfrac{64}{289}-\dfrac{225}{289}\\\\\\.\qquad=-\dfrac{161}{289}$

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Step-by-step explanation:

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