1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sonja [21]
1 year ago
12

Need help on the Sin(4x) part of the question please!!

Mathematics
1 answer:
Ksivusya [100]1 year ago
6 0

a. The equivalent expression for cos(4x) in terms of just x is 8cos⁴x - 8cos²x + 1

b. The equivalent expression for sin(4x) in terms of just x is 4sinxcos³x - 2sinxcosx

<h3>a. The equivalent trigonometric expression for cos(4x)</h3>

To find the trigonometric expression for cos(4x)

cos(4x) = cos[2(2x)]

Now from trigonometric identities

cos2Ф = 2cos²Ф - 1

Let 2x = Ф.

So, cos(4x) = 2cos²2x - 1

Also, cos2x = 2cos²x - 1

So, substituting cos2x into cos4x, we have

cos(4x) = 2cos²2x - 1

cos(4x) = 2[2cos²x - 1]² - 1

cos(4x) = 2[4cos⁴x - 4cos²x + 1] - 1

cos(4x) = 8cos⁴x - 8cos²x + 2 - 1

cos(4x) = 8cos⁴x - 8cos²x + 1

So, the equivalent expression for cos(4x) in terms of just x is 8cos⁴x - 8cos²x + 1

<h3>b. The equivalent trigonometric expression for sin(4x)</h3>

To find the expression for sin(4x)

sin(4x) = sin2(2x)

From trigonometric identities sin2Ф = 2sinФcosФ

Let 2x = Ф

So, sin(4x) = sin2(2x)

= 2sin2xcos2x

Since

  • sin2x = 2sinxcosx and
  • cos2x = 2cos²x - 1

Substituting these into the equation, we have

sin(4x) =  2sin2xcos2x

sin(4x) = (2sinxcosx)(2cos²x - 1)

sin(4x) = 4sinxcos³x - 2sinxcosx

So, the equivalent expression for sin(4x) in terms of just x is 4sinxcos³x - 2sinxcosx

Learn more about trigonometric expression here:

brainly.com/question/27904371

#SPJ1

You might be interested in
My meal cost $32.50 and I want to tip<br> 16%. What is my total for that meal?
nadya68 [22]

Answer:

Step-by-step explanation:

37.70

4 0
3 years ago
Read 2 more answers
I NEED HELP ASAP Use the Law of Detachment or the Law of Syllogism to draw a conclusion. 3. If Shauna is early for her meeting,
yuradex [85]
W = Shauna wakes up early
M = Shauna is early for her Meeting
P = Shauna gains a promotion

1. M -> P
2. W -> M
3. W
: . P
6 0
3 years ago
Solve for h.<br><br> h - 45 = -35
Ugo [173]

ℎ = ± \sqrt{x} 10\\

4 0
2 years ago
Read 2 more answers
Are the lengths of the side of the square and perimeter of the square related proportionally? Why or why not
telo118 [61]

Answer:

They are proportional

Step-by-step explanation:

becaue the length of one of the square's sides is 1/4 the perimeter

8 0
2 years ago
Homework: Algebra Re<br> Find the slope and the y-intercept<br> 6x-7y=15
umka21 [38]

Answer:

the slope is 6/7 the y-intercept is (0, -\frac{15}{7})

Step-by-step explanation:

I'm not 100% sure sorry lol.

3 0
3 years ago
Read 2 more answers
Other questions:
  • If (3, y) lies on the graph of y = -(2^x) then y=<br> 1/8<br> -6<br> -8
    12·2 answers
  • Need help solving this proportion....<br>x\4 = 5\7
    13·2 answers
  • I need to know how to simplify these problems.
    14·1 answer
  • Find the LCM for 24 and 30 using the cake method
    15·1 answer
  • Edward’s recipe for salad uses a ratio of 214 cups of lettuce to 12 lb of tomatoes. After reading the written response statement
    9·2 answers
  • As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $110. What is the minim
    7·1 answer
  • PLEASE HELP! WILL MARK BRAINLIEST
    14·1 answer
  • Given:<br> WXYZ is a rhombus.<br><br><br><br> If 5 = 20°, then 1 =<br><br> 20<br> 40<br> 70
    6·1 answer
  • Vincent has the following data:
    15·1 answer
  • Samson owes his friend
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!