I need step-by-step help with this homework... A) A circle has a radius of 15 in

Question

I need step-by-step help with this homework...

A) A circle has a radius of 15 inches. Find the length of the arc intercepted by a central angle of 120 degrees.

B) The minute hand of a clock moves from 12 to 2 o'clock or 1/6 of a complete revolution. Through how many degrees does it move? Through how many radians does it move?

C) If sin t= 1/3 and cos t= 2?2/3, find tan t, csc t, sec t, and cot t. Rationalize denominator where necessary.

D) Find the exact trigonometric value of -tan [(?/4)+15?)] without a calculator.

E) If f(?)= 2cos? - cos2?, find f(?/6)

Explanation / Answer

) R = 15 inch

Angle = 120 degree = 120*pi/180 radian = 2pi/3 radian

Then Arc length = (2pi/3)*15 = 31.4 inch

B) Total angle = 360 degree

In 1/6 revolution, Angle = 360/6 = 60 degree = 60*pi/180 radian = pi/3 radian

C) sin t= 1/3 and cos t= 2?2/3

tan t = sin t/cos t = 1/2?2

csc t = 1/sin t = 3

sec t = 1/cos t = 3/2?2

cot t = 1/tan t = 2?2

D) -tan [(?/4)+15?)] = -tan [(61?/4)] = -tan(5pi/4) = -tan(pi/4) = -1

E)

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