Question

True or false? Suppose alpha and beta are supplementary angles sin2(α)+cos2(β)=1 (justify your conclusion)

Answer 1

First, do you know what "supplementary" means?

Answer 2

Angles add up to 180

Answer 3

Alright.

We know that:
\[Cos^2(\alpha)+Sin^2(\alpha) = 1\]

This is true for any alpha, but notice that it's alpha in both.

Can you see how to use this to arrive at your answer?

Answer 4

Not really, I understand how to prove its complementary angle but I get confused with supplementary

Answer 5

Well, the key is that in the formula I gave, the arguments (what you put into it) of the sine and cosine must be exactly the same to equal one.

What this tells us about your question is:
\[\alpha = \beta\]

Of all the combinations of angles that you can add up to equal 180 degrees, only one combination exists where both are the same. 90 and 90.

But what this shows us is that only a special case of "supplementary angles" gets us the desired result. So being supplementary angles doesn't necessarily make the equation true.

Answer 6

So in most cases the trig equation is false?

Answer 7

For two supplementary angles, it's ONLY true when
\[\alpha = \beta = 90^o \]

Answer 8

Ah, I see. Mhmk then