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
artcher [175]
3 years ago
15

2sin²(x)-5cos(x)+1=0

Mathematics
1 answer:
Margarita [4]3 years ago
7 0
Remember the basic trig identity

<u />\sin^2 x + \cos^2 x = 1

We can move the cosine term to the right side to get

\sin^2 x = 1 - \cos^2 x

We can then replace \sin^2 x in the original equation and basically factor the resulting equation like a quadratic:

2(1 - \cos^2 x) - 5 \cos x + 1 = 0
(2 - 2 \cos^2 x) - 5 \cos x + 1 = 0
{-2} \cos^2 x - 5 \cos x  + 3 = 0
2 \cos^2 x + 5 \cos x - 3 = 0
(2 \cos x - 1)(\cos x + 3) = 0&#10;&#10;

Then, we can see that \cos x either equals \frac{1}{2} or -3. But since the range of cosine is only from [-1, 1], cosine can't equal -3 at all! So, you just have to solve for x when \cos x =  \frac{1}{2}, which is when

x = \{ \frac{\pi}{3}, \frac{5\pi}{3} \} + 2 \pi k | k \in \mathbb{Z}
(The last part of the solution says that k can be any integer.)

If you only want solutions in the range [0, 2\pi), then your answer is just

x = \frac{\pi}{3}, \frac{5\pi}{3}









You might be interested in
Can you help me find x
kifflom [539]
X = 30

hope that  helps

180 - 108 = 72

180 - 72 -43 = 65

triangle on the left 
Angles = 43,65,72

triangle on the right

180 - 65 = 115

180 - 115 - 35 = 30
so angles of triangle on the right = 30, 35, 115

x = 30 (vertical angles with the other angle of triangle on the right)



7 0
3 years ago
What is the solution of the system? Use substitution.
nekit [7.7K]
Substituting y=6x+2 into equation 3y - 18x =12 looks like:

3(6x + 2) - 18x = 12
18x + 6 - 18x = 12  distributive property left side
6 = 12  simplifying the left side

We now see a contradiction:   6 does not equal 12  What this tells us is that there is no solutions to this equation.  So choice 'C' ...
8 0
3 years ago
Read 2 more answers
Make an equation to represent the area of a square whose sides are given by the expression x + y
ki77a [65]

Answer:

x^2 + 2xy + y ^2

Step-by-step explanation:

A = a^2

a = x + y

(x + y) + (x + y)

x^2 + xy + xy + y^2

x^2 + 2xy + y ^2

4 0
3 years ago
QUESTION ATTACHED PLZ HELP NEEDED
saw5 [17]
Y = a (x + 3)² - 1

Let's take the point (-1;3)

3 = a ( -1 + 3)² - 1
3 = 4a - 1
4a = 4

Therefore a = 4/4 = 1

(x+3)² - 1
= x² + 6x + 9 - 1
= x² + 6x + 8

The answer would be y = x² + 6x + 8.

Hope this helps !

Photon
4 0
3 years ago
What is the solution to the inequality: -2x&gt;30
Greeley [361]

Answer: any neative number thats -16 and up

for example -16, -17,-18 etc

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Other questions:
  • Which of these are inequalities? choose 3 ​
    5·1 answer
  • 2c/15=8.8 Solve The Equation. What Is The Value Of "C"
    5·2 answers
  • The quotient of 5 subtracted from a number and 7 is 4.2?
    6·2 answers
  • How would you explain how to use a table to show this relationship, a pizza slice is $1.50 what is the relationship between the
    6·1 answer
  • Solve five and six eighths plus four and four fifths.
    7·2 answers
  • Hi bro how are you<br>kkjkjkjkjkjkjk
    5·1 answer
  • What is the point-slope form of 4x + 8y = 5?
    15·1 answer
  • Help me lol (please)
    15·2 answers
  • HELP!!!! If you help me with this you’ll be my favorite person ever
    15·1 answer
  • Part 4. NO LINKS!! Find the area of the shaded area shown. SHOW WORK PLEASE !! #21​
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!