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