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
kumpel [21]
3 years ago
15

Find the values of θ in the range 0≤θ≤360° which satisfy: 2 sin^2 θ - sinθ -1= 0

Mathematics
1 answer:
Sergio [31]3 years ago
7 0

Answer:

Step-by-step explanation:

Solving trig equations are just like solving "regular" equations. Let's get to it. First and foremost we are going to make a "u" substitution. You'll use that all the time in calculus, if you choose to go that route. Let

sin^2 \theta=u^2 and sinθ = u. Making the substitution, the equation becomes:

2u^2-u-1=0

That looks like something that can be factored, right? If you throw it into the quadratic formula you get the factors:

(u - 1)(2u + 1) = 0

By the Zero Product Property, either u - 1 = 0 or 2u + 1 = 0, so we will solve those, but not until after we back-substitute!

Putting sinθ back in for u:

sinθ - 1 = 0 so

sinθ = 1 and in the other equation:

2sinθ + 1 = 0 so

2sinθ = -1 and

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

Get out the unit circle and look to where the sinθ has a value of 1. There's only one place in your interval, and it's at 90 degrees.

Now look to where the sinθ has a value of -1/2. There are 2 places within your interval, and those are at 210° and 330°. Now you're done!

You might be interested in
Can someone plz help Me?
hammer [34]

Answer:

A

^{}

3 0
2 years ago
Read 2 more answers
Solve the formula <br> x − y = −8 for y.
laiz [17]

Answer:

y = x + 8

Step-by-step explanation:

x - y =  - 8

x + 8 = y

4 0
3 years ago
Can someone please help me with this problem, it is really confusing
levacccp [35]
Answer =-0.7x +0

Find the gradient by y2-y1/x2-x1
-14 -7/ 20- -10
-21/30
-0.7
And plug in the coordinates to find the y intercept
7= -0.7 (-10) + c
C=0
4 0
3 years ago
PLEASE HELP!!!!!!!!
Korolek [52]

Answer:

2π - 4√5

(= -2.66 to nearest hundredth).

Step-by-step explanation:

√(2π - 4√5)^2

= 2π - 4√5             (by the definition of a square root)

If you want an approximate value it is

-2.66 to the nearest hundredth

7 0
2 years ago
The boy the apartment building is filling a pool 30 ft long 20 feet wide and 5 feet deep it has been filled 4 ft deep how many m
inn [45]
Capacity of the pool = 30 x 20 x  5 = 3000 ft³

Amount of water already filled = 30 x 20 x 4 = 2400 ft²

Amount of water needed to full the pool = 3000 - 2400 = 600 ft²


---------------------------------------------------------------------------------------
Answer: 600 ft² of water is needed to fill up the pool.
---------------------------------------------------------------------------------------
4 0
3 years ago
Read 2 more answers
Other questions:
  • Which of the following numbers is read, "six thousand, nine hundred seven"?
    13·2 answers
  • 25 POINTS! WILL GIVE BRAINLIEST!
    7·1 answer
  • Find the slope of the points (5,-6) and (-1, 7).
    13·2 answers
  • A laboratory tested n = 98 chicken eggs and found that the mean amount of cholesterol was LaTeX: \bar{x}x ¯ = 86 milligrams with
    11·1 answer
  • A triangle has one side that measures 5 ft, one side that measures 8 ft, and one side that measures 11 ft.
    14·1 answer
  • HELP ASAP !!
    15·1 answer
  • What needs to be corrected in the following construction for copying∠ABC with point D as the vertex?
    5·2 answers
  • How does the value of the digit 3 in the number 63,297 compare to the value of the digit 3 in the number 60,325? Be sure to incl
    9·1 answer
  • When solving 8,411 ÷ 52, you decide to start by subtracting 100 groups of 52. What is the remainder?
    9·2 answers
  • REARRANGE EQUATIONS PLEASE HELP ITS DUE IN TOMORROW
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!