How do you rewrite sin37cos22+cos37sin22sin37cos22+cos37sin22 as a function of a single angle and then evaluate?

1 Answer
Sep 2, 2016

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°)