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
marysya [2.9K]
3 years ago
8

Find the exact values of sin2 θ for cos θ = 3/18 on the interval 0° ≤ θ ≤ 90°

Mathematics
1 answer:
mote1985 [20]3 years ago
6 0

Answer:

sin(2\theta)=\frac{\sqrt{35} }{18}

Step-by-step explanation:

Recall the formula for the sine of the double angle:

sin(2\theta)=2*sin(\theta)*cos(\theta)

we know that cos(\theta)=\frac{3}{18}, and that \theta is in the interval between 0 and 90 degrees, where both the functions sine and cosine are non-negative numbers. Based on such, we can find using the Pythagorean trigonometric property that relates sine and cosine of the same angle, what sin(\theta) is:

cos^2(\theta)+sin^2(\theta)=1\\sin^2(\theta)=1-cos^2(\theta)\\sin(\theta)=\sqrt{1-cos^2(\theta)} \\sin(\theta)=\sqrt{1-(\frac{3}{18} )^2}\\sin(\theta)=\sqrt{1-\frac{9}{324} }\\sin(\theta)=\sqrt{\frac{324-9}{324} }\\sin(\theta)=\sqrt{\frac{315}{324} }\\\\sin(\theta)=\frac{3}{18}\sqrt{35 }

With this information, we can now complete the value of the sine of the double angle requested:

sin(2\theta)=2*sin(\theta)*cos(\theta)\\sin(2\theta)=2*\frac{3}{18} \,\sqrt{35} \,\frac{3}{18}\\sin(2\theta)=\frac{2*3*3}{18*18}\,\sqrt{35} \\sin(2\theta)=\frac{\sqrt{35} }{18}

You might be interested in
How do I solve these equations?
lilavasa [31]

Answer:

Solve X

X=1/2     X=0.5

Solve V

W=0.0260416v

V=38.4W

3 0
3 years ago
Tamara texted a photo of a dolphin to 5 friends. She asked each of her 5 friends to text the photo to 5 more friends. The photo
Andreyy89
So 5
then 5 times 5
then 5 times 5 times 5
so it seems that for x rounds, there will be 5^x 

A: 4 rounds so 5^4=625 photos
B. see how many times 5 goes into 78125. the answer is 7 so 7 rounds
C. 1 million=1,000,000 so try big numbers
5^10=9,765,625 too big
5^9=1,9,53,125 too big
5^8=390625 too small
the minimum is 5^9 or 9 rounds

A:4
B:7
C:9

4 0
3 years ago
Which monomial is a perfect cube? <br> 16x6<br> 27x8 <br> 32x12 <br> 64x6
miss Akunina [59]
The fastest way is to just use a scientific calculator.

To do it without a calculator, use prime factorization.

I'll only do the second one which is the answer.

27 x 8

= 3^3 x 2^3 = 6^3

Which is a perfect cube.
5 0
3 years ago
Read 2 more answers
The marine green turtle has been known to swim 480 km (300 miles) in 10 days." How far, in kilometers, could a marine green turt
AnnyKZ [126]

Answer:

864

Step-by-step explanation:

You need to divide 480 by 10. Then multiply the answer which is 48 miles per day. Then take the 48 times 8 for the next 8 days. Then add the answer of that which is 384 and add it to 480.

Hope this helps.

7 0
3 years ago
F(x) = 3x2 + 6x – 18<br> Find f(10)
ozzi

Answer:

=

(

x

2

+

6

)

(

x

+

3

)

Step-by-step explanation:

[Grouping the first 2 terms together and the 2md 2 terms together.]

x

3

+

3

x

2

+

6

x

+

18

=

(

x

3

+

3

x

2

)

+

(

6

x

+

18

)

[Common factor]

=

x

2

(

x

+

3

)

+

6

(

x

+

3

)

{Taking the common bracket]

=

(

x

2

+

6

)

(

x

+

3

)

~Hope this helps! :)

5 0
3 years ago
Read 2 more answers
Other questions:
  • The town of Simpsonville has two tow truck companies. Company A charges an initial fee of $30 plus $2 per mile. Company B charge
    6·2 answers
  • What's an equation for A new plasma-screen television costs $5250. A family makes a down payment of $552 and pays off the balanc
    7·1 answer
  • In a proper fraction, is the numerator less than or greater than the denominator?
    11·1 answer
  • How do you solve the math equation y-y=m(x-x) for when you have to find the equation for an in and out table? i know how to get
    14·2 answers
  • Negative 2 multiply to blank equal negative fourteen
    8·1 answer
  • Whats the inverse and domain of the inverse
    6·1 answer
  • I need help with this.Thanks!
    15·1 answer
  • Compare the value of the 8 in 4,428.37 and 92.85
    7·2 answers
  • You win an online auction for a toy. Your winning bid of $35 is 70% of your maximum bid. How much more were you willing to pay f
    12·1 answer
  • PLEASE HELP ME ASAP!!!!!!!!!!!!!!!
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!