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ACT Math: Trigonometry Drill 1, Problem 1. What is the length of y?
ACT Math: Coordinate Geometry Drill 1, Problem 2. Solve the inequality and determine which solution is shown on the number line.
ACT Math 4.1 Trigonometry 228 Views
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Description:
ACT Math: Trigonometry Drill 4, Problem 1. Simplify the expression.
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
Full Transcript
- 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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