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
andriy [413]
2 years ago
7

Please help me thank you

Mathematics
1 answer:
Hoochie [10]2 years ago
3 0

Answer:

\large\boxed{\sin2\theta=\dfrac{\sqrt3}{2},\ \cos2\theta=\dfrac{1}{2}}

Step-by-step explanation:

We know:

\sin2\theta=2\sin\theta\cos\theta\\\\\cos2\theta=\cos^2\theta-\sin^2\thet

We have

\sin\theta=\dfrac{1}{2}

Use \sin^2\theta+\cos^2\theta=1

\left(\dfrac{1}{2}\right)^2+\cos^2\theta=1\\\\\dfrac{1}{4}+\cos^2\theta=1\qquad\text{subtract}\ \dfrac{1}{4}\ \text{from both sides}\\\\\cos^2\theta=\dfrac{4}{4}-\dfrac{1}{4}\\\\\cos^2\theta=\dfrac{3}{4}\to\cos\theta=\pm\sqrt{\dfrac{3}{4}}\to\cos\theta=\pm\dfrac{\sqrt3}{\sqrt4}\to\cos\theta=\pm\dfrac{\sqrt3}{2}\\\\\theta\in[0^o,\ 90^o],\ \text{therefore all functions have positive values or equal 0.}\\\\\cos\theta=\dfrac{\sqrt3}{2}

\sin2\theta=2\left(\dfrac{1}{2}\right)\left(\dfrac{\sqrt3}{2}\right)=\dfrac{\sqrt3}{2}\\\\\cos2\theta=\left(\dfrac{\sqrt3}{2}\right)^2-\left(\dfrac{1}{2}\right)^2=\dfrac{3}{4}-\dfrac{1}{4}=\dfrac{3-1}{4}=\dfrac{2}{4}=\dfrac{1}{2}

You might be interested in
Find the distance between parallel lines whose equations are y = x - 6 and y = x + 8.
Sidana [21]

Answer:

14

Step-by-step explanation:

Distance between y2 = x + 8 and y1 = x - 6

y2 - y1 = (x + 8) - (x - 6) = 14

8 0
2 years ago
Why would negative numbers not make sense for the values of the variables
Naily [24]
One reason that negative numbers would not make sense for values of the variables is that the solution having a negative value is not valid. It might be that the expression represents a real word problem and a negative value will not make any sense. Hope this helps.
7 0
3 years ago
Read 2 more answers
346772.99378 x 222222666886=
nordsb [41]

Answer:

7.706081948 lowecase10uppercase16

Step-by-step explanation:

I hope it helps u.

6 0
3 years ago
American car makers produce 5,650,000 cars each year. In a report, Ben wrote that Americans made 6,550,000 cars. What mistake di
Degger [83]
Ben wrote the number for the hundred thousands place in the millions place
3 0
3 years ago
Which of the following polynomials has solution that are real numbers ?
slava [35]
I think that the only polynomial that has a solution that are real numbers is:

B) x² + 4x + 3 = 0
(x + 3) (x + 1) → x² + 1x + 3x + 3 → x² + 4x + 3

(x+3) = 0 → x = -3

(x + 1) = 0 → x = -1

Real numbers are number that are whole numbers, rational and irrational numbers, positive and negative numbers, and even zero. 
7 0
3 years ago
Other questions:
  • a child find 29 nickels and dimes. how many dimes are there if the total value of the coins are $2.10?
    8·2 answers
  • 24% of 289=<br> Estimate using a rate per 100
    12·1 answer
  • If quadrilateral ABCD is congruent to quadrilateral EFGH, then what corresponding side is congruent to side EF? (5 points)
    7·1 answer
  • Find the 27th term in the arithmetic sequence of 59,56,53,50
    14·1 answer
  • The side length of a square is (8-√10) inches long. What's the area of the square.
    9·1 answer
  • 100 POINTS PLEASE HELP ASAP!!!!!
    8·2 answers
  • Express 75cm/s in m/s​
    5·1 answer
  • The length of one base of a trapezoid is 19 meters and the length of the median is 23 meters. Find the length of the other base,
    10·2 answers
  • 16) What is the four interior angle of the quadrilateral?
    13·1 answer
  • .46 as fraction again in simplest
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!