Question

Find the value of each trigonometric ratio

Answer 1

The value of each trigonometric ratio is

`$\sin A=(15)/(17), \ \cos A=(8)/(17), \ \tan A =(15)/(8)`

`$\csc A=(17)/(15), \ \sec A=(17)/(8), \ \cot A =(8)/(15)`

Solution:

The given triangle is right triangle.

AC (hypotenuse) = 34, AB (adjacent) = 16, BC (opposite) = 30

To find the trigonometric ratios:

Using trigonometric formulas for right triangle,

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

`$\sin A=(BC)/(AC)`

`$\sin A=(30)/(34)=(15)/(17)`

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

`$\cos A=(AB)/(AC)`

`$\cos A=(16)/(34)=(8)/(17)`

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

`$\tan A=(BC)/(AB)`

`$\tan A=(30)/(16)=(15)/(8)`

`$\csc A =(1)/(\sin A)`

`$\csc A =(17)/(15)`

`$\sec A =(1)/(\cos A)`

`$\sec A =(17)/(8)`

`$\cot A =(1)/(\tan A)`

`$\cot A =(8)/(15)`

Hence the value of each trigonometric ratio is

`$\sin A=(15)/(17), \ \cos A=(8)/(17), \ \tan A =(15)/(8)`

`$\csc A=(17)/(15), \ \sec A=(17)/(8), \ \cot A =(8)/(15)`