Question

If tan a = 9／40
use trigonometric identities to find the values of sin a and cos a.​

Answer 1

see explanation

Explanation:

Given

tan a =
`(9)/(40)` =
`(opposite)/(adjacent)`

We require the hypotenuse h

Using Pythagoras' identity

h² = 9² + 40² = 81 + 1600 = 1681 ( take square root of both sides )

h =
`√(1681)` = 41 , thus

sin a =
`(opposite)/(hypotenuse)` =
`(9)/(41)`

cos a =
`(adjacent)/(hypotenuse)` =
`(40)/(41)`