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Question
Find the value of the trigonometric functions for the following:
cos θ = `2/3`, θ lies in the I quadrant
Solution
We know that cos2θ + sin2θ = 1
`(2/3)^2 + sin^2theta` = 1
`4/9 + sin^2theta` = 1
sin2θ = `1 - 4/9`
sin2θ = `(9 - 4)/9 = 5/9`
sin θ = `+- sqrt(5)/3`
Since θ lies in the I quadrant all trigonometric functions are positive.
sin θ = `sqrt(5)/3`, cosec θ = `1/sintheta = 3/sqrt(5)`
cos θ = `2/3`, sec θ = `1/costheta = 3/2`
tan θ = `sintheta/costheta = (sqrt(5)/3)/(2/3) = sqrt(5)/2`
cot θ = `costheta/sintheta = (2/3)/(sqrt(5)/3) = 2/sqrt(5)`
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