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ACT Math 4.1 Trigonometry 228 Views


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Description:

ACT Math: Trigonometry Drill 4, Problem 1. Simplify the expression.

Language:
English Language

Transcript

00:02

For a good time, solve this shmoopy question.

00:05

Simplify. sin4⍺ - cos4⍺ << sine to the fourth alpha minus cosine to the fourth alpha>>

00:10

And here are our answer choices...

00:16

Okay, the trick lies in recognizing the fact that 2 squared equals 4.

00:22

It means we can express sine to the fourth alpha minus cosine to

00:26

the fourth alpha as sine squared alpha squared

00:29

minus cosine squared alpha squared... because they're the same thing.

00:33

Now we need to call on our good friend - the

00:35

difference of two squares formula: x squared minus y squared equals x minus y times x plus y.

00:43

If we pretend that sin squared alpha is x

00:45

and cos squared alpha is y, we can simplify it to:

00:49

sin squared alpha minus cosine squared alpha times sin squared alpha PLUS cosine squared

00:55

alpha. We also know that (sin2⍺

00:59

+ cos2⍺) = 1 from the fundamental trig identities.

01:03

Now all we're left with is (sin2⍺ -- cos2⍺)...

01:07

...which happens to be answer D.

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