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
Taking a test will mark braniniliest
Vlad [161]

Answer:

whats the question?

8 0
2 years ago
Read 2 more answers
Please Help! What is the distance between points (2, 8) and (7, 5)? Round to the nearest tenth of a unit.
zavuch27 [327]
Distance formula is like pythagoren ahtoerem
D=\sqrt{(7-2)^{2}+(5-8)^{2}}
the distance between oints (x1,y1) and (x2,y2) is
D=\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}
(2,8) and (7,5)
D=\sqrt{(7-2)^{2}+(5-8)^{2}}
D=\sqrt{(5)^{2}+(-3)^{2}}
D=\sqrt{25+9}
D=\sqrt{34}
apxos
D=5.8309....

round
D=5.8 units


6 0
3 years ago
Read 2 more answers
What is the equation of the line with m = 3 and b = 8.25?
quester [9]
Y=3x + 8.25
...................
6 0
3 years ago
Mile markers along the highway tell drivers how many miles they have traveled from one location to another. Suppose Daniel sees
agasfer [191]
The answer to you question is 74.
3 0
3 years ago
What is this Simplify as √16y¹6
ELEN [110]

Answer:

6y^1^6

Step-by-step explanation:

I hope this has Helped :)

7 0
1 year ago
Other questions:
  • Helppppppppp plzzzzzzzzzzzzzzzzzzzz!
    15·1 answer
  • You have completed 4 miles of a 10 mile race in 32 minutes. At this pace, how long will it take you to complete the entire race?
    6·2 answers
  • What is (17-3)x(14-6)-22
    10·2 answers
  • An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to usi
    7·1 answer
  • Plz help I’m a loser at math
    11·2 answers
  • Consider the function f(x) = x2 + 12x + 11. x-intercepts?
    10·2 answers
  • There are 12 students in a classroom, including the triplets Joey, Chloe, and Zoe. If 3 of the 12 are randomly selected to give
    7·1 answer
  • Help me with this please. I typed it on my iPad
    7·2 answers
  • Please help no link please help no links
    12·1 answer
  • I NEED HELP ASAP, thanks
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!