Question

If cosθ=b/√a²+b²,0<θ<90,find the value of sinθ and tanθ.

Answer 1

Given, $\bf{cos\theta=\frac{b}{\sqrt{a^2+b^2}}}$

we know,
cosθ = base/hypotenuse = b/√(a²+b²)

base = b , hypotenuse = √(a² + b²)

from Pythagoras theorem,

perpendicular = √(hypotenuse² - base²)

= $\sqrt{(\sqrt{a^2+b^2})^2-b^2}$

= a

we know,
sinθ = perpendicular/hypotenuse

so, sinθ = a/√(a² + b²)

and tanθ = perpendicular/base = a/b

Answer 2

On applying Pythagoras Theorem

we got the required angle of measurement

as shown in the attachment.