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
Write an equation of the parabola in vertex form. <br><br>No LINKS!!!! ​
marissa [1.9K]

9514 1404 393

Answer:

  y = -16x² +180

Step-by-step explanation:

The vertex appears to be the high point of the graph, (0, 180). Then the vertex form equation is ...

  y = a(x -0)² +180

The value of 'a' can be found using the other given point. Substituting for x and y, we have ...

  164 = a(1 -0)² +180

  -16 = a

Then the complete simplified vertex form equation is ...

  y = -16x² +180

8 0
2 years ago
The Regency Hotel has enough space at its entrance for six taxicabs to line up, wait for guests, and then load passengers. Cabs
maksim [4K]

Answer:

The appropriate solution is:

(1) 22.81 minutes

(2) 0.171

Step-by-step explanation:

According to the question, the values will be:

The service rate of guess will be:

= 5+3.5

= 8.5 \ minutes

The mean arrival rate will be:

\lambda =\frac{60}{5}

  =7.5 \ cabs/hr

The mean service rate will be:

\mu= 7.05 \ cabs/hr

(1)

The average time a cab must wait will be:

⇒ W_q=22.95-\frac{1}{7.05}

⇒       =\frac{161.798-1}{7.05}

⇒       =\frac{160.798}{7.05}

⇒       =22.81 \ minutes

(2)

The required probability will be:

⇒ P(X\geq 6)=\frac{1-2.115}{1-7.5}

⇒                  =\frac{-1.1115}{-6.5}

⇒                  =0.171

6 0
3 years ago
Plzz im dumb i need your help
likoan [24]

Answer:

a

Step-by-step explanation:

3 0
3 years ago
$10 + ($6-n) if n =$3<br> What is the final product <br> Of this mathematical question?
kap26 [50]
If n = $3 then plug it in
$10 + ($6-$3)
$6-$3 = $3
$10 + $3 = $13
5 0
3 years ago
Read 2 more answers
What is the value of H
never [62]

Answer:

h = 55

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

the 2 unknown interior angles = 180 - 2h ( straight angle ), hence

the sum of the 3 angles

180- 2h + 180 - 2h + 40 = 180

400 - 4h = 180 ( subtract 400 from both sides )

- 4h = - 220 ( divide both sides by - 4 )

h = 55


6 0
3 years ago
Other questions:
  • 3(x + 4) - x/2 when x = 2
    12·2 answers
  • Can someone please tell me how to solve this?
    9·1 answer
  • Help my math teacher created thistest and I don’t know how to do any of this
    6·1 answer
  • Need help with 1 question
    5·1 answer
  • Which expression did he write
    14·1 answer
  • If there was a system where 5 points was equivalent to $1 how many points would $43 be?
    13·2 answers
  • Help pls and thank you! :))
    9·2 answers
  • Elle was asked to find the missing measure of an interior angle of a heptagon. A heptagon has angles x, 116 degrees, 115 degrees
    14·2 answers
  • (Please someone help me!) (No links!)
    8·1 answer
  • In a survey of 1,600 people who owned a certain type of car, 1,120 said they would buy
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!