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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?
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
Full Transcript
- 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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