Question

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

Answer 1

-
`(161)/(289)`

Explanation:

Using the trigonometric identity

cos(2x) = 2cos²x - 1

given cosx =
`(8)/(17)`, then

cos(2x) = 2(
`(8)/(17)`)² - 1

= 2 ×
`(64)/(289)` -
`(289)/(289)`

=
`(128)/(289)` -
`(189)/(189)` = -
`(161)/(289)`

Answer 2

Answer:
`\bold{-(161)/(289)}`

Explanation:

Given: cos x =
`(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 =
`-(15)/(17)`

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

`cos (2x) = cos^2 x - sin^2 x\\\\.\qquad=\bigg((8)/(17)\bigg)^2-\bigg(-(15)/(17)\bigg)^2\\\\\\.\qquad=(64)/(289)-(225)/(289)\\\\\\.\qquad=-(161)/(289)`