Question

Show that the sine or cosine value of an angle measuring 48 degrees is equivalent to the sine or cosine value of that same angle measured in radians and state the value of the function

Answer 1

You must convert degrees to radians before evaluating trig functions. An angle of 48 degrees equals 48·π/180 = 4π/15 radians, so

- sin(48°) = sin(4π/15) ≈ 0.7431448255,
- cos(48°) = cos(4π/15) ≈ 0.6691306064.

If instead you feed the number 48 to the trig function as radians, you get different values:

- sin(48) ≈ −0.7682546613,
- cos(48) ≈ −0.6401440008.

Thus sin(48°) (or cos(48°)) is not equal to sin(48) (or cos(48)) unless you first convert degrees to radians. If you meant something else, tell me and I’ll adjust.