Question

CosA=3/5
Apply three identities and get all the values of trigonometric functions

Answer 1

`(1)sin\: \theta =(4)/(5) \\\\(2)tan\: \theta =(4)/(3)\\\\(3)cosec\: \theta =(5)/(4)\\\\(4)sec\: \theta =(5)/(3)\\\\(5)cot\: \theta =(3)/(4)`

Explanation:

If Cos A
`=(3)/(5)`

Recall that:

`cos \theta =(Adjacent)/(Hypotenuse) \\$Therefore:\\Adjacent=3\\Hypotenuse=5`

By knowledge of Pythagorean Triples, we know that the Opposite of A=4.

`(1)sin\: \theta =(Opposite)/(Hypotenuse)=(4)/(5) \\\\(2)tan\: \theta =(Opposite)/(Adjacent)=(4)/(3)\\\\(3)cosec\: \theta =(1)/(sin\theta)=(5)/(4)\\\\(4)sec\: \theta =(1)/(cos\theta)=(5)/(3)\\\\(5)cot\: \theta =(1)/(tan\theta)=(3)/(4)`