Determine sin θ = 1/4, 0 < θ <π/2; cosθ?

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Answer 1 · 2018-02-19T06:40:33

#costheta = sqrt15/4#

Use the theorem

#sin^2theta + cos^2theta = 1#

Here put , #sintheta = 1/4#

#(1/4)^2 + cos^2theta = 1#

# 1/16 + cos^2theta = 1#

# cos^2theta = 1 - 1/16#

# cos^2theta = 15/16#

# costheta = +-sqrt(15/16)#

# costheta = +-sqrt15/4#

Since theta lies between 0° and 90° , the value of #costheta# should be positive.

So , #costheta = sqrt15/4#