A current rotates a circular paddle with diameter 8 feet at 20 revolutions per m

Question

A current rotates a circular paddle with diameter 8 feet at 20 revolutions per minute. What is the speed of the current in miles per hour? What is the angular velocity of the paddle in radians? The terminal side of theta lies on the given line y = -x in the second quadrant. Find the values of the six trigonometric functions of theta. If sin theta = 4/5, and theta elementof QII, find: cos theta, sin 2 theta, and sin theta/2 If cos alpha = -3/5 with alpha having a terminal side in QIII, and sin beta = 4/5 with beta having a terminal side in QII, find: sin(alpha + beta) and tan(alpha - beta).

Explanation / Answer

y=-x

y/x=-1

tan theta=y/x=-1

cot theta=1/tan theta=-1

csc theta=sqrt(1+cot2theta) = sqrt2

sin theta=1/csc theta =1/sqrt2

cos theta=sqrt(1-sin2theta)=-1/sqrt2

sec theta=1/cos theta=-sqrt 2

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