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ACT Math 1.3 Trigonometry 274 Views


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Description:

ACT Math: Trigonometry Drill 1, Problem 3. Can you find the cosine?

Language:
English Language

Transcript

00:02

And here is your shmoop de jour...

00:04

Find the cosine 105 degrees.

00:06

And here are your options...Hm, great question.

00:09

Alright let's use the difference formula for cosine.

00:13

Cosine times A minus B equals cosine

00:16

A times cosine B plus sine A

00:20

time sine B. Now have to decide what the values A and B are.

00:25

What are two friendly angles?

00:28

As in nice trig values that have a different of 105

00:32

150 - 45 is 105, though A equals 150 and B equals

00:37

45. Now I can plug it into the difference formula for cosine.

00:41

We can figure out what cosine of 150 degrees is based on the cosine of

00:46

30 degrees. The 150 degrees is just a mulitple of 30 degrees

00:50

but in the second quadrant or cosine is negative...the cosine of 150

00:55

equals negative cosine 30 degrees. Cosine of 30 degrees equal square root of

00:59

3 over 2

01:00

so cosine to 150 degrees is negative root 3

01:04

over 2. Cosine of 45 degrees is the square root of two over two.

01:09

We can find sine of 150 degrees based on sine of

01:12

30 degrees because once again a 150 is a multiple of 30 degrees

01:16

since sin is still positive in Quadrant 2...

01:20

...Sine 150 degrees equals the same value sine of thirty degrees.

01:24

Sine 30 is one half and so is sin 150

01:28

Sine 45 is the square root of 2 over 2

01:32

we have negative square root three over two times the square root

01:36

2 over two plus one half time through 2 over 2

01:40

Simplified we get negative square root of six over four-plus the square root of

01:45

two over 4

01:46

which equals root 2 minus root 6 all over four.

01:50

Option C is our answer.

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