Question

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

Answer 1

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):

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

             

Answer 2

Answer:

- $\frac{161}{289}$

Step-by-step explanation:

Using the trigonometric identity

cos(2x) = 2cos²x - 1

given cosx = $\frac{8}{17}$, then

cos(2x) = 2($\frac{8}{17}$)² - 1

           = 2 × $\frac{64}{289}$ - $\frac{289}{289}$

          = $\frac{128}{289}$ - $\frac{189}{189}$ = - $\frac{161}{289}$