How do you find the remaining trigonometric functions of #theta# given #cottheta-=1/2# and #costheta>0#?

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How do you find the remaining trigonometric functions of #theta# given #cottheta-=1/2# and #costheta>0#?

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Answer 1 · 2017-07-07T03:47:09

#cot t = 1/2# --> tan t = 2
Use trig identity:
#cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 4) = 1/5#
#cos t = 1/sqrt5 = sqrt5/5# --> (because cos t > 0)
#sin^2 t = 1 - cos^2 t = 1 - 1/5 = 4/5#
#sin t = +- 2/sqrt5 = +- (2sqrt5)/5#
tan t = 2 , then, t is in Quadrant 1, and sin t is positive
#sin t = (2sqrt5)/5#
#sec t = 1/(cos t) = sqrt5#
#csc t = 1/(sin t) = sqrt5/2#

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How do you find the remaining trigonometric functions of #theta# given #cottheta-=1/2# and #costheta>0#?

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