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]
2 years ago
10

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

Mathematics
1 answer:
yan [13]2 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
The vertices of the trapezoid are the origin along with A(4p,4q), B(4r,4q), and C(4s,0). Find the midpoint of the midsegment of
Nesterboy [21]

Check this attachment

8 0
3 years ago
1 hundreth is how many times greater than 1 thousandths? Pls helppp
Verdich [7]

Answer:

1 hundreths is 10 times greater than 1 thousandths.

Step-by-step explanation:

just like 100 is ten times greater than 10.

4 0
3 years ago
Read 2 more answers
Is the equation y=-2x+5 in standard form? Explain
anyanavicka [17]
The equation, y = -2x + 5, is not in standard form. The standard form of a linear line is ax + by = c. This equation is in slope - intercept form, which is y = mx + b. 
7 0
2 years ago
Create a function that has two distinct roots: - 3/4 and -1?
asambeis [7]

Step-by-step explanation:

Sorry I cant get any more answers but I really hope that this helps

3 0
2 years ago
Read 2 more answers
Select two ratios that are equivalent to 4:18
nalin [4]

Answer

B and E

Mark as brainly if possible!!

8 0
3 years ago
Read 2 more answers
Other questions:
  • Sarah is 27 years old and is retiring at the age of 65. When she retires, she estimates that she will need a semiannual income f
    8·1 answer
  • Question 1(Multiple Choice Worth 4 points) Which of the following is a rational number? square root 97square root 98, square roo
    11·1 answer
  • Find the cartesian coordinates of the given polar coordinates. then plot the point. (a) (− 2 , 5π/4)
    8·1 answer
  • A right triangle has a hypotenuse of length 20 and a leg of length 12. what is the length of the other leg? if necessary, round
    7·1 answer
  • 8 minus a number<br> N/8<br> 8-n<br> 8/n <br> 8n
    9·2 answers
  • The school band will sell pizzas to raise money for new uniforms. The supplier charges $143 plus $5 per
    6·1 answer
  • 1. Simplify the rational expression (5 3/2)(5 1/2)
    14·1 answer
  • Solve the equation: 2 sqrt x-3-5 =1
    14·1 answer
  • Over the past 20 years the prices of homes have increased by 30%, resulting in the average price of a house being $500,000. What
    15·2 answers
  • Arrange the steps to perform this subtraction operation in the correct order.
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!