Question

Evaluate the six trigonometric functions of the angle 0.

sin 0 =
csc 0=
cos 0 =
sec 0 =
tan 0=
cot 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√(14)=\text{opposite}`

Using trigonometric ratio formula:

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

`$\sin\theta =(4√(14) )/(18)`

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

`$\csc\theta =(18)/(4√(14) )`

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

`$\cos \theta=(10)/(18)`

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

`$\sec \theta=(18 )/(10)`

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

`$\tan \theta=(4√(14) )/(10)`

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

`$\cot \theta=(10)/(4√(14) )`