Video: Using Trigonometric Values of Special Angles to Evaluate Trigonometric Expressions

Find the value of sin² 45 + cos² 45.

01:21

Video Transcript

Find the value of sine squared 45 plus cos squared 45.

To help us find the value of sine squared 45 plus cos squared 45, we’re actually gonna use one of our Pythagorean trigonometric identities. I’m just gonna show you three of them and then I’ll show you the one that we’re actually gonna be using.

Okay, so the example of our Pythagorean trig identities are sine 𝜃 plus cos squared 𝜃 equals one, tan squared 𝜃 plus one equals sec squared 𝜃, and one plus cot squared 𝜃 is equal to cosec squared 𝜃.

And now to actually solve this problem, find the values of sine squared 45 plus cos squared 45, we’re actually gonna be using this top one, which is sine squared 𝜃 plus cos squared 𝜃 is equal to one. And this is actually sometimes known as the fundamental Pythagorean trigonometric identity.

So if you see how we’re going to use it, well actually the way we gonna use it is that our 𝜃 is gonna be equal to 45. Cause as you can see in the identity, we’ve got sine squared 𝜃 plus cos squared 𝜃 equals one, so still the same 𝜃 in each part, where in ours we’ve got 45 in each part.

So therefore, we can say that sine squared 45 plus cos squared 45 must be equal to one. And we’ve actually achieved that because we’ve used our top Pythagorean trigonometric identity, which is sin squared 𝜃 plus cos squared 𝜃 equals one.

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