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
Aleks04 [339]
3 years ago
12

How can i solve sin(7x)=sin(5x)?

Mathematics
1 answer:
andrew11 [14]3 years ago
8 0
   
\displaystyle  \\ 
\texttt{The equation has three solutions.} \\  \\ 
S1: \\ 
\sin(7x) = \sin(5x) \\ 
7x = 5x \\ 
7x-5x=0 \\ 
2x=0 \\ 
\boxed{x_1 = 0^o} \\ 
Check:  \\ 
\sin(7\cdot 0)= \sin(0) = 0~~and~~\sin(5\cdot 0)= \sin(0) = 0 





\displaystyle S2: \\ 
\sin(7x) = \sin(5x) \\ 
\sin(180-\alpha)=\sin(\alpha) ~~\Longrightarrow~~ \sin(90+\beta)=\sin(90-\beta) \\ 
\Longrightarrow~~  \frac{7x + 5x}{2} = 90^o \\  \\ 
 \frac{12x}{2} = 90^o \\  \\ 
6x = 90^o \\  \\ 
x_2 =  \frac{90}{6} \\  \\ 
\boxed{x_2 = 15^o }\\  \\ 
Check: \\ 
\sin(7\cdot 15^o) = \sin(105^o)=\sin(180^o-105^o)=\sin(75^o)=\sin(5\cdot 15^o)



\displaystyle S3: \\ 
\sin(7x) = \sin(5x) \\ 
\sin(180+\alpha)=\sin(360-\alpha) ~~\Longrightarrow~~ \sin(270+\beta)=\sin(270-\beta) \\ 
\Longrightarrow~~  \frac{7x + 5x}{2} = 270^o \\  \\ 
 \frac{12x}{2} = 270^o \\  \\ 
6x = 270^o \\  \\ 
x_3 =  \frac{270}{6} \\  \\ 
\boxed{x_3 = 45^o }\\  \\ 
Check: \\ 
\sin(7\cdot 45^o) = \sin(315^o)=\sin(360^o-45^o)=\sin(180+45^o)=  \\  = \sin(225^o) = \sin(5 \cdot 45^0)



You might be interested in
Please Please Please Help Me On These 2 Math Questions!!!!! I GIVE THANKS!!!!
Mars2501 [29]
A. After the mod. One wall is “x” longer than original (horizontal in diagram) and the other is “x” shorter (vertical)
(30+x)(30-x)

b. He original area = 30 x 30 = 900 sq. ft.
The mod. Area is (30+6)(30-6) = 36x24= 764 sq. ft.

So the room was largest to begin with when it was a square
3 0
3 years ago
The equation of the line of best fit of a scatter plot is
Verizon [17]

Answer:

-6

Step-by-step explanation:

y intercept is -6 because formula of gradient is y=mx+c.......c is the y intercept

5 0
4 years ago
Can someone please help me with this?
icang [17]
16/4= 4 so the 16+4=20 and 20 is the answer
3 0
2 years ago
Please help me with the picture attached also, I am so confused
antoniya [11.8K]

Answer:

I can't see the picture?

Where is it???

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
A ball was dropped in a height of 81cm.Everytime it hits the ground,it bounces 2/3 of its previous height.What height will the b
kkurt [141]

Answer:

i think 16

Step-by-step explanation:

this is what makes sense to be boo<3

4 0
3 years ago
Other questions:
  • Which equation exemplifies the commutative property of multiplication??
    12·1 answer
  • Find the area of the triangle QRS.
    8·2 answers
  • Consider the given rectangle with heightequals4timeswidth. Let x be the width of the rectangle. Write an expression for the​ per
    6·1 answer
  • In a certain freshman class, the number of girls is 83 less than twice the number of boys(b). The total number of students in th
    13·2 answers
  • A How does matter change from one state to another?
    8·1 answer
  • The machinist's goal was to increase his production by at least 10% each day. Assume he achieved his goal. If he was able to mac
    10·2 answers
  • If a watch cost $40 and you pay 6.5% sales tax, how much will the tax be
    8·2 answers
  • What is 3/4 divided by 1/3?
    7·1 answer
  • The price of a four-star dinner was $100 two decades ago. A report says that a dinner is 250% of what it was 20 years ago, how m
    9·1 answer
  • Lamonte has 50 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!