Question

Write the expression as the sine, cosine, or tangent of an angle.

sin 57° cos 13° - cos 57° sin 13°
Select one:
a. cos 70°
b. cos 44°
c. sin 44°
d. sin 70°

Answer 1

Use this formula: sin (x-y) = sinx cosy - cosx siny

sin57 cos13 - cos57 sin13 = sin (57 -13) = sin (44)

Answer 2

Answer: The correct option is (c) sin 44°.

Step-by-step explanation: We are given to write the following expression as the sine, cosine or tangent of an angle :

`T=\sin 57^\circ\cos13^\circ-\cos57^\circ\sin13^\circ.`

We will be using the following trigonometric formula :

`\sin (A+B)=\sin A\cos B-\cos A\sin B.`

Therefore, we get

`T\\\\=\sin 57^\circ\cos13^\circ-\cos57^\circ\sin13^\circ\\\\=\sin(57^\circ-13^\circ)\\\\=\sin 44^\circ.`

Thus, the required expression can be written in sine of an angle of measure 44°.

Option (c) is CORRECT.