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
Marianna [84]
2 years ago
8

−10sin(x)=−4csc(x)+3

Mathematics
1 answer:
tatiyna2 years ago
7 0

-10 sin(x) = -4 csc(x) + 3

Recall that csc(x) = 1/sin(x) :

-10 sin(x) = -4/sin(x) + 3

Multiply both sides by sin(x) :

-10 sin²(x) = -4 + 3 sin(x)

Move everything to one side:

10 sin²(x) + 3 sin(x) - 4 = 0

Factorize the left side:

(2 sin(x) - 1) (5 sin(x) + 4) = 0

Then we have two cases,

2 sin(x) - 1 = 0   or   5 sin(x) + 4 = 0

Solve for sin(x) :

sin(x) = 1/2   or   sin(x) = -4/5

Solve for x :

• if sin(x) = 1/2, then

x = arcsin(1/2) + 2nπ   or   x = π - arcsin(1/2) + 2nπ

x = π/6 + 2nπ   or   x = 5π/6 + 2nπ

• if sin(x) = -4/5, then

x = arcsin(-4/5) + 2nπ   or   x = π - arcsin(-4/5) + 2nπ

x = -arcsin(4/5) + 2nπ   or   x = π + arcsin(4/5) + 2nπ

(where n is any integer)

You might be interested in
How many positive integer factors of 100! are multiples of 2 or 3?
elena-s [515]

Positive integer factors of 100:

1, 2, 4, 5, 10, 20, 25, 50, 100

Now find if they are a multiple of 2 or 3.

2, 4, 10, 20, 50, 100

That is 6 factors.

3 0
3 years ago
Evaluate the expression for the given values. p + q when p = 15 and q = 12
SSSSS [86.1K]

Substitute 15 for p and 12 for q in p + q. We get 15 + 12, or 27.

3 0
3 years ago
Rounding 8,469 to one decimal place
wlad13 [49]

Answer:

do you mean "8.469"? of so 8.5

Step-by-step explanation:

assuming the comma should be a decimal

3 0
3 years ago
Does this table represent a function? Why or why not? <br><br> Pick A,B,C or D
stepladder [879]
The answer would be D.

In order for a table to represent a function, each x-value needs to pair with exactly one y-value and no more.

In the table shown here, none of the x-values repeat and all of them pair with a unique y-value which means that it’s a function.
6 0
3 years ago
Help me put these numbers from least to greatest 1 1/3, -5/6, 0, -2/3, -1 from least to greatest.
Degger [83]

Answer:

-5,6,-2/3,1 1/3,0

Step-by-step explanation:

I think this how it goes try it out or not i need help to

6 0
2 years ago
Other questions:
  • To fit in an existing frame, the length, x, of a piece of glass must be longer than 12 cm but not longer than 12.2 cm. Which ine
    14·2 answers
  • Which is bigger ? 3/4 or 2/3?
    6·2 answers
  • What is greater 1 4/6 or 1 14/21
    15·2 answers
  • Gas costs $6 per gallon and diesel costs $8 per gallon. You have at most $85 to spend on fuel. You must purchase at least 12 gal
    14·1 answer
  • find the point slope equation for the line that passes through the points (-6,24)and (5,-31) use the first point in your equatio
    10·2 answers
  • There are 38 people in line to ride the bumper cars. 8 people can go in each round. How many people will ride in the last round?
    11·1 answer
  • Laboratory experiment shows that the life of the average butterfly is normally distributed with a mean of 18.8 days and a standa
    6·1 answer
  • What is the square root of 8 rounded to the nearest tenth?
    10·1 answer
  • A truck is painting Traffic lines along a highway the truck paints 8 miles of lines in 3 hours at the rate how many miles can a
    9·1 answer
  • Plz help me with this question
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!