Find sin(2x), cos(2x), and tan(2x) from the given information. sin(x) = −8/17 , x in Quadrant III

Question

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Answer 1

sin(x) = -8/17 in the 3rd quadrant.

Calculate the reference angle as

xRef = arcsin(8/17) = 28.07 deg.

The actual angle, is therefore

x = 180 + 28.07 = 208.07 deg.

Hence,

2x = 2*208.07 = 416.145 deg.

This is equivalent to

θ = 416.145 - 360 = 56.145 deg, in the 1st quadrant.

Answer:

sin(2x) = sin(56.145) = 0.83

cos(2x) = cos(56.145) = 0.56

tan(2x) = tan(56.145) = 1.49