Question

Find the Sin, Cos, and Tan of the following angle:

Answer 1

$\sin 45^\circ=\frac{-1}{\sqrt{2} }, \ \cos45^\circ=\frac{1}{\sqrt{2} }, \ \ \tan 45^\circ=-1$

Solution:

In the given right triangle,

θ = 45°

Opposite side to θ = –1

Adjacent side to θ = 1

Hypotenuse = $\sqrt{2}$

Using basic trigonometric ratio formulas,

$\sin \theta=\frac{\text { Opposite }}{\text { Hypotenuse }}$

$\sin 45^\circ=\frac{-1}{\sqrt{2} }$

$\cos \theta=\frac{\text { Adjacent }}{\text { Hypotenuse }}$

$\cos45^\circ=\frac{1}{\sqrt{2} }$

$\tan \theta=\frac{\text { Opposite }}{\text { Adjacent }}$

$\tan 45^\circ=\frac{-1}{1}=-1$

Therefore,

$\sin 45^\circ=\frac{-1}{\sqrt{2} }, \ \cos45^\circ=\frac{1}{\sqrt{2} }, \ \ \tan 45^\circ=-1$