Question

How do you rewrite `sin37cos22+cos37sin22` as a function of a single angle and then evaluate?

Answer 1

Use the formula for the sine of a sum to get `sin(59°)`. This trigonometric function does not have a simple form so an evaluation requires a calculator.

Explanation:

Formula for the sine of a sum:

`sin(color(blue)(a)+color(gold)(b))=sin(color(blue)(a))cos(color(gold)(b))+cos(color(blue)(a))sin(color(gold)(b))`

Thus

`sin(color(blue)(37°)+color(gold)(22°))=sin(color(blue)(37°))cos(color(gold)(22°))+cos(color(blue)(37°))sin(color(gold)(22°))`

So your trigonometric expression is

`sin(color(blue)(37°)+color(gold)(22°))=sin(59°)`