Please help!!!

Question

Given that cos A=5/13 and that <A is located in the fourth quadrant determine the exact value for sin A and tan A.

Answer 1

cosA = 5/13

<A is located in fourth quadrant.

Recall the basic trigonometric ratios.

cosA = [ adjacent side/hypotenuse]

From the Pythagorean theorem,

Opposite side = √[(hypotenuse)² - (adjacent side)²]

= √[(13)² - (5)²]

= √[169 - 25]

= √144

= 12

In fourth quadrant sine and tangent are negative.

sinA = opposite side/hypotenuse

= -12/13

tanA = opposite side/adjacent side

= - 12/5

sinA = -12/13 and tanA = -12/5.