Find the exact values of the indicated trigonometric function. cos[-5 pi/6] Use

Question

Find the exact values of the indicated trigonometric function. cos[-5 pi/6] Use the unit circle to find all the exact values of theta that make the equation true in the indicated interval. a) sec theta = - Squareroot 2, 0 lessthanorequalto theta lessthanorequalto 2 pi b) cos theta = - Squareroot 3/2, 0 lessthanorequalto theta lessthanorequalto 2 pi For the given functions, find the amplitude (if applicable), period, and phase shift. Sketch the graph over the indicated interval and label all x-intercepts and max and min points. a) y = -sin(2x), - pi/2 lessthanorequalto x lessthanorequalto pi/2 b) y = 3/2 cos(pi x), over at least one period c) y = -tan[x - pi/2], - pi lessthanorequalto x lessthanorequalto pi. Find an equation for each graph. Assume no phase shift has taken place.

Explanation / Answer

1 . Cos(-5pi/6) = cos(5pi/6) = cos(pi - pi/6)=-cos (pi/6)=-sqrt3 /2

2.a. sec theta=-sqrt2

1/cos theta=- sqrt2

Cos theta=-1/sqrt2

Theta=3pi/4/5pi/4

b. Cos theta=-sqrt3/2

Theta=cos-1(-sqrt3/2) =5pi/6, 7pi/6

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