What is a possible cofunction identity for (sin theta)?

To find a possible cofunction identity for sin(theta), we need to understand what a cofunction is. In trigonometry, the cofunction of an angle is the value of a trigonometric function of its complementary angle. The complementary angle of theta is 90 degrees minus theta (90° - theta), or in radians (π/2 - theta).

The cofunction identity for sin(theta) is cos(π/2 - theta). So, a possible cofunction identity for sin(theta) is cos(π/2 - theta).

To verify this identity, we can use the definitions of sin and cos functions in a right-angled triangle. Let's consider a right-angled triangle with one angle as theta. The side opposite to theta is represented by the vertical side (a) and the side adjacent to theta is represented by the horizontal side (b).

According to the definitions:

sin(theta) = a / hypotenuse
cos(π/2 - theta) = b / hypotenuse

Since the hypotenuse is the common length in both equations, we can conclude that sin(theta) = cos(π/2 - theta).

Therefore, cos(π/2 - theta) is a possible cofunction identity for sin(theta).

A possible cofunction identity for sin(theta) is cos({{pi}}/2 - theta).