Question

Which of these equations is always true?

sin(x) = cos(x)
sin(x) = cos(90°-x)
sin(x) = cos(180°-X)
sin(x) = cos(360° - x)

Answer 1

sin(x) = cos(90°-x)

Explanation:

Looking at the graphs of sin(x) and cos(x), you can see that the peaks of the graph are separated by a value of pi/2. If you convert that value into degrees, then the two graphs are separated by 90°. Another way of thinking is from the unit circle. sin(x) = 1 at 90°, and cos(x)=1 at 0°. The difference is still 90°