Use a reference triangle to find the given angle. 1) cos ^-1(-1/(sqrt2))=? Find

Question

Use a reference triangle to find the given angle. 1) cos ^-1(-1/(sqrt2))=? Find the value of tan(cos^-1((sqrt7)/3))

Explanation / Answer

1. If the angle is in the Fourth Quadrant, then we know that... sin(?) < 0 and cos(?) > 0. Then... cos(?) = 4/5 sin(?) = -3/5 tan(?) = sin(?)/cos(?) = -3/4 Hence... tan(2?) = 2tan(?)/(1 - tan²(?)) = 2(-3/4)/(1 - (-3/4)²) = -24/7 2. That would be... tan(x/2) = sin(x)/(1 + cos(x)) Where x/2 = 105 ? x = 210.... tan(210/2) = sin(210)/(1 + cos(210)) = -1/(2(1 - v(3)/2)) * 2/2 = -2/(2(2 - v3)) = -1/(2 - v3) [You might want to revise your choices since all of them are incorrect...] 3. 1 + cos(2a) = 2/(1 + tan²(a)) Use... cos(2a) = 2cos²(a) - 1

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