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
marusya05 [52]
3 years ago
10

Solve sin 0 + 1 = cos20 on the interval 0 ≤ 0 < 2pi. Show work please!

Mathematics
1 answer:
yan [13]3 years ago
7 0

Answer:

\theta=\frac{\pi}{2},\frac{3\pi}{2}\frac{2\pi}{3}\frac{4\pi}{3}

Step-by-step explanation:

You need 2 things in order to solve this equation:  a trig identity sheet and a unit circle.

You will find when you look on your trig identity sheet that

cos(2\theta)=1-2sin^2(\theta)

so we will make that replacement, getting everything in terms of sin:

sin(\theta)+1=1-2sin^2(\theta)

Now we will get everything on one side of the equals sign, set it equal to 0, and solve it:

2sin^2(\theta)+sin(\theta)=0

We can factor out the sin(theta), since it's common in both terms:

sin(\theta)(2sin(\theta)+1)=0

Because of the Zero Product Property, either

sin(\theta)=0 or

2sin(\theta)+1=0

Look at the unit circle and find which values of theta have a sin ratio of 0 in the interval from 0 to 2pi.  They are:

\theta=\frac{\pi}{2},\frac{3\pi}{2}

The next equation needs to first be solved for sin(theta):

2sin(\theta)+1=0 so

2sin(\theta)=-1 and

sin(\theta)=-\frac{1}{2}

Go back to your unit circle and find the values of theta where the sin is -1/2 in the interval.  They are:

\theta=\frac{2\pi}{3},\frac{4\pi}{3}

You might be interested in
Write the equation of a circle with a center at (-2, 3) and a radius of 4.
Ivan

Answer:

The equation of a circle:

(x+2)^2+(y-3)^2 = 16

Step-by-step explanation:

The equation of a circle:

(x-h)^2+(y-k)^2 = r^2

(where the center is known as (h,k) and the radius, known as r).

-Since you already have the center and the radius, use them for the equation of a circle:

Center: (-2,3)

Radius: 4

(x+2)^2+(y-3)^2 = 4^2

After you have the equation of a circle, simplify the radius by the exponent 2 :

(x+2)^2+(y-3)^2 = 16

So, you have found the equation of a circle.

5 0
3 years ago
\WILL GIVE BRAINLY, PLEASE HELP
MissTica

Answer:

....

Step-by-step explanation:

3 0
3 years ago
Can someone please help me with this
UNO [17]
Ok so we know that student tickets cost $5, and adult tickets cost $8. We also know that the total no. of tickets sold was 150.

Let's make the amount of student tickets sold be S, and the no. of adult tickets sold be A.

We know that tickets sales amounted to $1,020, so:
8A + 5S = 1020
And:
A + S = 150. Multiply this by 5;
5A + 5S = 750

When you subtract the two equations;
(8A+5S) - (5A+5S) = 1020-750
So 3A = 270
A = 90
So 90 adult tickets were sold.
S = 150 - 90
= 60
So 60 student tickets were sold (although you don't need this as part of your answer)

Hope this helped
4 0
3 years ago
,,sarah is building a birdhouse the nail she uses are one inch long.the wood board is 1 foot long . how many times smaller are t
tamaranim1 [39]
The board is 12x larger in length than the nails. (Since the width of the board and nails are unknown, I am assuming you mean the length, not area difference)
3 0
3 years ago
Read 2 more answers
Answer 1 or answer 2?
Viefleur [7K]

Answer:

2 Function B

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Other questions:
  • Fiona has $18 to spend. She spent $4.25, including tax, to buy a notebook. She needs to save $9.75, but she wants to buy a snack
    6·1 answer
  • What does tan^2(theta) mean?
    13·1 answer
  • Solve for d in the following equation: c(ad) + x = bd + ad(yz)
    14·1 answer
  • X^2=3x+3 using the quadratic formula,show steps
    7·1 answer
  • Number d plz solve it
    12·1 answer
  • A = (1,5)<br> C = (1.75, 2.5)<br> B = (?)<br> What are the coordinates of point B in the diagram
    7·1 answer
  • Is 0.0309 greater than 0.05?
    11·1 answer
  • Solve for x. 2.5x=50
    14·2 answers
  • In the equation y=3x+15<br> What is the slope and y intercept?
    13·1 answer
  • if your parents shop in maryland the sales tax is 6% if they buy $180 worth of groceries what is there total
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!