SOLUTION: Use the cofunction identities to evaluate the expression. sin^2 (18 Degrees) + sin^2 (40 Degrees) + Sin^2 (50 Degrees)+ sin^2 (72 Degrees) I'm honestly stumped after hours of

Algebra ->  Trigonometry-basics -> SOLUTION: Use the cofunction identities to evaluate the expression. sin^2 (18 Degrees) + sin^2 (40 Degrees) + Sin^2 (50 Degrees)+ sin^2 (72 Degrees) I'm honestly stumped after hours of      Log On


   

Question 710533: Use the cofunction identities to evaluate the expression.
sin^2 (18 Degrees) + sin^2 (40 Degrees) + Sin^2 (50 Degrees)+ sin^2 (72 Degrees)
I'm honestly stumped after hours of attempts, will anyone assist me in my struggle?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
In a right triangle, the two acute angles are complementary,
meaning that their measures add up to 90.
The way sine and cosine were defined based on a right triangle,
sine of an angle is the cosine of the complement.
(It works if you define sine and cosine based on the unit circle too).
Something similar happens with tangent and cotangent,
and with secant and cosecant.
For all the trigonometric functions the function of an angle
equals the cofunction of the complement.
Those are the cofunction identities.

Since 18%5Eo%2B72%5Eo=90%5Eo,
angles measuring 18%5Eo and 72%5Eo are complementary,
and sin%2872%5Eo%29=cos%2818%5Eo%29.
Then

Also , since 40%5Eo%2B50%5Eo=90%5Eo,
angles measuring 40%5Eo and 50%5Eo are complementary,
and sin%2850%5Eo%29=cos%2840%5Eo%29.
Then

Putting it all together:

=