Sign In
Ask Question
Armani Adkins
Mathematics
13 December, 06:13
Find an identity for cos (4t) in terms of cos (t)
+3
Answers (
1
)
Colten
13 December, 06:35
0
So you can do this multiple ways, I'll do this the way that I think makes sense the l most easily.
Cos (0) = 1
Cos (pi/2) = 0
Cos (pi) = - 1
Cos (3pi/2) = 0
Cos (2pi) = 1
Now if you multiply the inside by 4, the graph oscillates more violently (goes up and down more in a shorter period).
But you can always reduce it.
Cos (0) = 1
Cos (4pi/2) = cos (2pi) = 1
Cos (4pi) = Cos (2pi) = 1 (Any multiple of 2pi = = 1)
etc ...
the pattern is that every half pi increase is now a full period as apposed to just a quarter of one. That's in theory.
Now that you know that, the identities of Cosine are another beast, but mathematically.
You have.
Cos (2*2t) = Cos^2 (2t) - Sin^2 (2t)
Sin^2 (t) = - Cos^2 (t) + 1 ... (all A^2+B^2=C^2)
Cos (2*2t) = Cos^2 (t) - (-Cos^2 (t) + 1)
Cos (2*2t) = 2Cos^2 (2t) - 1
2Cos^2 (2t) - 1 = 2 (Cos^2 (t) - Sin^2 (t)) ^2 - 1
(same thing as above but done twice because it's cos ^2 now)
convert sin^2
2Cos^2 (2t) - 1 = 2 (Cos^2 (t) + Cos^2 (t) - 1) ^2 - 1
2 (2Cos^2 (t) - 1) ^2 - 1
2 (2Cos^2 (t) - 1) (2Cos^2 (t) - 1) - 1
2 (4Cos^4 (t) - 2 (2Cos^2 (t)) + 1) - 1
Distribute
8Cos^4 (t) - 8Cos^2 (t) + 1
Cos (4t) = 8Cos^4-8Cos^2 (t) + - 1
Comment
Complaint
Link
Know the Answer?
Answer
Not Sure About the Answer?
Find an answer to your question 👍
“Find an identity for cos (4t) in terms of cos (t) ...”
in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers
You Might be Interested in
What is x-2y=-1 and 2x+y=4 using elimination step by step
Answers (1)
Forrest orders 5 boxes of toothbrushes. If he had 135 toothbrushes altogether, how many are in each box?
Answers (1)
A box of cereal states that there are 99 calories in a 3/4 cup serving. What is the unit rate for calories per cup? How many calories in 3 cups of cereal
Answers (1)
Change the equation 2x+3y=1,470 into slope-intercept form
Answers (1)
An employee is paid a gross yearly salary of $57,000.00. How much does this employee earn each month? A. $4,795.00 B. $4,780.00 C. $4,750.00 D. $5,105.00
Answers (1)
New Questions in Mathematics
5x - (x+4) = 10-2 (x-8) solve for x
Answers (1)
Which pairs of numbers represent a number and its reciprocal? 1 and 1 2/3 and - 3/2 1/2 and 5 6 and 1/6 -4/7 and - 7/4
Answers (1)
Which of the following lists is in the correct order from largest to smallest? A) 82, 80, 13, - 2 B) - 6, - 3, 1, 2 C) 35, 13, - 7, - 1 D) 18, 21, - 8, - 11
Answers (1)
2log4-log3+2logx-4=0
Answers (1)
F=G m1m2/r^2 solve for G
Answers (1)
Home
»
Mathematics
» Find an identity for cos (4t) in terms of cos (t)
Sign In
Sign Up
Forgot Password?