Question

Given that cos 26 degrees= 0.899, write the sine of a complementary angle

Answer 1

Complementary = angle+other angle = 90 degrees

90-26(given)=64
There is only one complimentary angle to any other angle, so 64 is the only other one. Sin(64)=.899

Sin(64)=cos(26)
This is because cosine and sine are actually THE SAME. Cosine exists because there's sine. Cosine is sine moved over on a graph a bit. The sine of any angle, plus 90degrees (or pi/2) is equal to the cosine of that angle

Cos(x)=sin(x+90) <--degrees
Cos(x)=sin(x+pi/2) <-- radians(from unit circle)

Unit circle has 90 degrees at pi/2 which is why that works. Using a graphing calculator in degrees, you'd use the first equation I gave to prove that they're equal, and in radian mode, you'd use the second one. Cosine is Co in front of sine. Co meaning complimentary, which is why the problem equals each other when solved