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Question
if `sin theta = 1/sqrt2` find all other trigonometric ratios of angle θ.
Solution
Given `sin theta = 1/sqrt2`
We have to find all the trigonometric ratios.
We have the following right angle triangle.
From the above figure,
Base = `sqrt("Hypotenuse"^2 - "Perpendicular"^2)`
`=> BC = sqrt("AC"^2 - sqrt(AB)^2)`
`=> BC= sqrt((sqrt2)^2 - 1^2)`
`=> BC= 1`
`cos theta = (BC)/(AC) = 1/sqrt2`
`cosec theta = (AC)/(AB) = sqrt2/1 = sqrt2`
`sec theta = (AC)/(BC) = sqrt2/1 = sqrt2`
`tan theta = (AB)/(BC) = 1/1 = 1`
`cot theta = (BC)/(AB) = 1/1 = 1`
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