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ACT Math 3.5 Trigonometry 250 Views


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Description:

ACT Math: Trigonometry Drill 3, Problem 5. Simplify the expression.

Language:
English Language

Transcript

00:02

Here's your shmoop du jour, brought to you by Alpha. Please don't tell it that it looks

00:07

like a "cute little fishie." It hates that.

00:11

Simplify: 2sin alpha over cos alpha times the quantity 1 minus tan squared alpha.

00:16

And here are your potential answers...

00:21

Alright, we're going to have to work with

00:22

a lot of trig here to simplify this... if you aren't too great with your trig formulas

00:26

and identities, we'd recommend you hit pause and review them before you tackle this problem.

00:32

formula is just too messy...

00:32

formula is just too messy...

00:32

So… let's start simplifying it first.

00:32

Ok, here goes. First we can separate this nasty thing into two fractions multiplied

00:36

by each other

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This gives us 2 times sine alpha over cosine alpha times 1 over the quantity 1 minus tangent

00:44

squared alpha. Because we know our identities backward and

00:47

forward, we know that tangent alpha equals sin alpha over cosine alpha...

00:52

...leaving us with 2 times tangent alpha over the quantity 1 minus tangent squared alpha.

00:58

But wait - doesn't that look like our formula for tangent 2 alpha?

01:02

Why yes, it does. Tangent 2 alpha is our answer. Answer E.

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