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

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) (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 .
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 ,
angles measuring and are complementary,
and .
Then

Also , since ,
angles measuring and are complementary,
and .
Then

Putting it all together:

=
RELATED QUESTIONS
using pythagorean identity to siplify the following expressions. a) cos^2 30 degrees + (answered by richard1234)

Use trigonometrical identities to expand and simplify if possible, the following: 1) cos (answered by swincher4391)

sin^2 87 degrees + cos^2 87 degrees... evaluate... (answered by jim_thompson5910)

Evaluate 4sec 180 degrees - 2 sin ^2 270... (answered by lwsshak3)

Help!! Use the properties of the trigonometric functions to find the exact value of... (answered by Alan3354)

Evaluate the expression sin 270... (answered by tommyt3rd)

Find the exact value of the expression without a calculator. {{{sin^2(40 degrees) +... (answered by greenestamps)

I'm trying to use the sum and differences identities to write this expression as a sine,... (answered by Alan3354)

The expression cos^2 40 degrees - sin^2 40 degrees has the same value as (1) sin 20... (answered by jim_thompson5910)