Thread: Exact values of decimals

Hi there, I am having trouble understanding how to find the exact trigonometric values of decimals. For example, find the exact value of tan 67.5. I realize the answer is 1 + √2 but I can't figure out how to get that. Thanks!

Try doubling the angle, and then turning around and using half-angle formulas for the tangent.

Originally Posted by markymark

Hi there, I am having trouble understanding how to find the exact trigonometric values of decimals. For example, find the exact value of tan 67.5. I realize the answer is 1 + √2 but I can't figure out how to get that. Thanks!

This is an exercise in Trig identities. First notice that 90 - 67.5 = 22.5 which is half of 45. In degrees, tan(90-x) = cot(x). So it is enough to calculate tan(22.5). Then use half-angle. You have tan(22.5) = (1-cos(45))/sin(45) .