Question

What is the relationship between the sine of an angle and cosine of the other acute angle in the same triangle? Will this be true every time? Why or why not?

Answer 1

Consider in triangle as given below:

sin(A) = opposite/hypotenuse = BC/AC
cos(B) = adjacent/hypotenuse = BC/AC

Now, both of them have the same hypotenuse and both will be equal. As you have seen already both the values are same.
Thus, the relationship between the sine of an angle and cosine of the other acute angle in the same triangle is shown below. And this ill this be true every time.