Question

Evaluate the six trigonometric functions of the angle 0.

Answer 1

Given:

Right triangle

To find:

The six trigonometric functions of θ

Solution:

Hypotenuse = 18

Adjacent side to θ = 10

Opposite side to θ = ?

Using Pythagoras theorem:

$\text {Hypotenuse}^2 = \text{adjacent}^2+\text{opposite}^2$

$18^2 =10^2+\text{opposite}^2$

$324=100+\text{opposite}^2$

Subtract 100 from both sides.

$224=\text{opposite}^2$

Taking square root on both sides.

$4\sqrt{14}=\text{opposite}$

Using trigonometric ratio formula:

$\sin\theta =\frac{\text{opposite }}{\text{hypotenuse}}$

$\sin\theta =\frac{4\sqrt{14} }{18}$

$\csc\theta =\frac{\text{hypotenuse}}{\text{opposite }}$

$\csc\theta =\frac{18}{4\sqrt{14} }$

$\cos \theta=\frac{\text { adjacent side }}{\text { hypotenuse }}$

$\cos \theta=\frac{10}{18}$

$\sec \theta=\frac{\text { hypotenuse }}{\text { adjacent side }}$

$\sec \theta=\frac{18 }{10}$

$\tan \theta=\frac{\text { opposite side }}{\text { adjacent side }}$

$\tan \theta=\frac{4\sqrt{14} }{10}$

$\cot \theta=\frac{\text { adjacent side }}{\text { opposite side }}$

$\cot \theta=\frac{10}{4\sqrt{14} }$