Question

The expression sin 57° is equal to

(1) tan 33°

(3) tan 57°

(2) cos 33°

(4) cos 57°

Answer 1

`cos(33^(\circ))`

Explanation:

Given

`sin(57^(\circ))`

Required

Determine an equivalent expression

In trigonometry:

`sin(\theta)= cos(90^(\circ) - \theta)`

In
`sin(57^(\circ))`

`\theta=57^(\circ)`

Substitute
`57^(\circ)` for
`\theta`

in
`sin(\theta)= cos(90^(\circ) - \theta)`

`sin(57^(\circ))= cos(90^(\circ) - 57^(\circ))`

`sin(57^(\circ))= cos(33^(\circ))`

Hence, the equivalent expression is:
`cos(33^(\circ))`