The point (- 1/3, 1/2) is a point on the terminal side of angle theta in standar

Question

The point (- 1/3, 1/2) is a point on the terminal side of angle theta in standard position. Find the exact values of the six trigonometric functions of angle theta Find all values of x for which each of the following is undefined. (a) f(x) = tan(3x) (b) g(x) = csc x (c) q(x) = sin(5x) (d) P(x) = sec(2x + 3) Given that sin theta = -0.75, find 7 sin(theta + 2 pi) - 3 sin(theta + 8 pi) + 6 sin(theta - 10 pi) Given that theta is in quadrant II and tan theta = -8/7, find cos theta Sketch the graph of each of the following: (a) f(x) = sin x (b) g(x) = cos x (c) q(x) = tan x (d) P(x) = cot x (e) W(x) = sec x (f) R(x) = csc x

Explanation / Answer

8. (-1/3,1/2)

Tan theta=y/x=-3/2

Opposite=3 adjacent=2

Hypotenuse=sqrt13

Sin theta=opposite/hypotenuse=-3/sqrt13

Cos theta=adjacent/hypotenuse=2/swrt13

Csc theta=1/sin theta=-sqrt13/3

Sec theta=1/cos theta=sqrt13/2

Cot theta=1/tan theta=-2/3

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