Question

if `sin theta = 1/sqrt2`  find all other trigonometric ratios of angle θ.

Answer 1

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`