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Question

 please help.?

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.

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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.