Trigonometric functions of complementary angles
key notes :
If w and z are complementary angles, these identities are true:
sin(w) = cos(z)
cos(w) = sin(z)
These identities imply:
sec(w) = csc(z) because sec(w)= 1/cosw = 1/sinz = csc(z)
tan(w) = cot(z) because tan(w)= sinw/cosw = cosz/sinz = cot(z)
Learn with an example
sin(x)=0.8. If x and y are complementary, what is cos(y)?
Since y and x are complementary, the sine of y is equal to the cosine of x.
cos(y)=sin(x)=0.8
sin(x)=0.9. If x and y are complementary, what is cos(y)?
Since y and x are complementary, the sine of y is equal to the cosine of x.
cos(y)=sin(x)=0.9
sin(x)=0.9. What is cos(90°–x) ?
90°–x and x are complementary, since their angles sum to 90°.
So, the cosine of 90°–x is equal to the sine of x.
cos(90°–x)=sin(x)=0.9
let’s practice!
