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Evaluate the six trigonometric functions of the angle 0.

sin 0 =
csc 0=
cos 0 =
sec 0 =
tan 0=
cot 0=

Evaluate the six trigonometric functions of the angle 0. sin 0 = csc 0= cos 0 = sec-example-1

1 Answer

4 votes

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) )

User John Doeherskij
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