Whenever 𝑠𝑖𝑛𝜃=1, the value of 𝑐𝑜𝑠𝜃 is:

The value of cos𝜃 when sin𝜃=1 is 0.

Here's why:

The sine and cosine of an angle are defined as the y and x coordinates, respectively, of a point on the unit circle. The unit circle is a circle with a radius of 1 that is centered at the origin of the coordinate plane.

When sin𝜃=1, this means that the point is at the very top of the unit circle. This is the point (0,1). The x-coordinate of this point, which represents cos𝜃, is 0. Therefore, when sin𝜃=1, cos𝜃=0.