Question

If sinθ =11/61, find the values of cosθ using trigonometric identity.

Answer 1

GIVEN:
sinθ =11/61
By using trigonometric identity
sin²θ + cos²θ = 1
cosθ = √(1-sin²θ)
cos θ = √(1 - (11/61)²
cos θ = √(1 -121/3721
cosθ =√(3721 - 121)/ 3721
cosθ = √3600/3721
cosθ = 60/61
[ √3600 = 60, √3721 = 61]

Hence, the value of cosθ = 60/61

HOPE THIS ANSWER WILL HELP YOU....

Answer 2

$\bf{Given,}$
sinθ = 11/61

We know, sinθ = perpendicular/hypotenuse = 11/61
first of all we have to find $\bf{base}$,
$\bf{base=\sqrt{hypotenuse^2-perpendicular^2}}$
Base = √(61² - 11²) = √(61 + 11)(61 - 11) = √(72 × 50)
Base = 6 × 10 = 60

Hence, cosθ = base/hypotenuse = 60/61
$\bf{cos\theta=\frac{60}{61}$