Let θ be an angle in quadrant IV such that secθ=8/5. Find the exact values of cotθ and sinθ .

Answer 1

In this problem the angle given is located in the four quadrant . The secθ= 8/5, keep in mind that secθ= 1/cosθ or reciprocal of cosine = x and y= sine in the unit circle.

cos θ= 5/8. reciprocal of the secθ , now I need to find the sinθ=?

in order to find the sinθ , I going to use the trig identity sin(θ)^2=1-cos(θ)^2

sin(θ)^2 = 1- (5/8)^2= 1-25/64

sin(θ)= +- √ 64- 25/64 = -√39 /8 this is the value of the sine(θ), this value of the sin(θ), is neg in the 4th quadrant.

1) Cot (θ) = cosθ/sinθ=. 5/8 / √39 /8. = 5/8 x. 8/√9 = 5/√39 = Rationalization.

5/√39 x √39/√39= 5√39/(39)...............This is the value of the cot(θ) also neg in the 4 quadrant.

I

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I θ

I

Answer 2

sec theta=8/5=1/cos

1/cos=1.6

1.6*cos=1

cos=.769

theta=320.28deg

quad4

cot theta=cos/sin=-1.20365067

sin theta=-.6390363497