Question

Express cos A and tan A in terms of sin A.

Answer 1

To express cos A in terms of sin A:

From the identity sin² A + cos² A = 1:

cos² A = 1 – sin² A

Taking the square root (assuming A is an acute angle):

`cos A = sqrt(1 - sin^2 A)`

Now, to express tan A in terms of sin A:

We know `tan A = sin A/cos A`

Substitute the expression for cos A derived above:

`tan A = sin A/sqrt(1 - sin^2 A)`

`cos A = sqrt(1 - sin^2 A)` and `tan A = sin A/sqrt(1 - sin^2 A)`