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
rosijanka [135]
3 years ago
8

How do you solve cos(pi/24) using Half-Angle formulas, and leaving in simplified form?

Mathematics
1 answer:
adoni [48]3 years ago
6 0
\cos \frac{\theta}{2}=\sqrt{\frac{1+\cos \theta}{2}}
\\
\\ \cos{\frac{\pi}{24}}=\cos{\frac{\frac{\pi}{12}}{2}}=\sqrt{\frac{1+\cos \frac{\pi}{12}}{2}}= \sqrt{ \frac{1}{2}+ \frac{\cos \frac{\pi}{12}}{2}  } 
\\
\\ \cos{\frac{\pi}{12}}=\cos{\frac{\frac{\pi}{6}}{2}}=\sqrt{\frac{1+\cos \frac{\pi}{6}}{2}}= \sqrt{ \frac{1}{2}+ \frac{ \frac{ \sqrt{3} }{2} }{2}  } =\sqrt{ \frac{2}{4}+  \frac{ \sqrt{3} }{4}   } = \sqrt{\frac{ 2+\sqrt{3} }{4} } = 
\\
\\ =\frac{ \sqrt{2+\sqrt{3}} }{2} 


\cos{\frac{\pi}{24}}= \sqrt{ \frac{1}{2}+ \frac{\cos \frac{\pi}{12}}{2}  } = \sqrt{ \frac{1}{2}+ \frac{\frac{ \sqrt{2+\sqrt{3}} }{2}}{2}  } = \sqrt{ \frac{2}{4}+ \frac{ \sqrt{2+\sqrt{3}} }{4}}  } =\sqrt{ \frac{ 2+\sqrt{2+\sqrt{3}} }{4}}  } 
\\
\\\cos{\frac{\pi}{24}}=\frac{\sqrt{2+\sqrt{2+\sqrt{3}}}} {2}


You might be interested in
Calcule:
fgiga [73]
E and f were a little complicated.

5 0
2 years ago
Union President Abraham Lincoln set the Union's first naval goal when he declared a blockade of the Southern coasts. His plan wa
Schach [20]

Answer:

OK sounds good

Step-by-step explanation:

6 0
3 years ago
Solve for V:<br><br>V+9/15=0
astraxan [27]
V= 0.4

9/15=0.6

0.6+0.4=0
8 0
3 years ago
A doctor released the results of clinical trials for a vaccine to prevent a particular disease. In these clinical​ trials, 200,0
CaHeK987 [17]

Answer:

1) No, there is  not  enough evidence to support the claim that the vaccine was effective (P-value=0.104) .

The null and alternative hypothesis are:

H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0

being the subindex 1 for the experimental group and subindex 2 for the control group.

2) Test statistic z=-1.26

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the vaccine was effective.

Then, the null and alternative hypothesis are:

H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0

The significance level is 0.01.

The sample 1 (experimental group), of size n1=100000 has a proportion of p1=0.0002.

p_1=X_1/n_1=21/100000=0.0002

The sample 2 (control group), of size n2=100000 has a proportion of p2=0.0003.

p_2=X_2/n_2=30/100000=0.0003

The difference between proportions is (p1-p2)=-0.0001.

p_d=p_1-p_2=0.0002-0.0003=-0.0001

The pooled proportion, needed to calculate the standard error, is:

p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{21+30}{100000+100000}=\dfrac{51}{200000}=0.00026

The estimated standard error of the difference between means is computed using the formula:

s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.00026*0.99974}{100000}+\dfrac{0.00026*0.99974}{100000}}\\\\\\s_{p1-p2}=\sqrt{0+0.0000000025}=\sqrt{0.0000000051}=0.000071

Then, we can calculate the z-statistic as:

z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.00009-0}{0.000071}=\dfrac{-0.00009}{0.000071}=-1.26

This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):

P-value=P(z

As the P-value (0.104) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is  not  enough evidence to support the claim that the vaccine was effective.

6 0
2 years ago
In the following expression, both AAA and BBB are variables that can take positive values.
ololo11 [35]

The value to increase is keeping A constant and decreasing the value of B

<h3>What are fractions?</h3>

Fractions are written as a ratio of two integers. For instance a.b is a fraction where a and b are integers.

In the fraction a/b, the numerator is and the denominator is b. If the value of the denominator is decreasing the fraction will increase but if the value of the denominator is increasing the fraction will decrease.

Given the expression A + 2/B, the higher the value of B provided such that that A is constant, the higher the expression. Hence the expression that will cause the value to increase is keeping A constant and decreasing the value of B

Learn more on fractions here: brainly.com/question/17220365

#SPJ1

8 0
2 years ago
Other questions:
  • In referring to snipers what is 2 minutes left mean
    7·1 answer
  • What is the area in cm^2 of the circle shown above
    13·1 answer
  • NEED help with homework
    11·1 answer
  • 4 - (-8) =<br> What is the answer
    10·1 answer
  • A wooden flooring strip is 20 1/2 inches long. If you cut off 4 3/4 inches from one end what will be the new length of the strip
    9·1 answer
  • Howard needs new gutters for the front and both sides of his home. The front of the house is 50 ft 8 in., and each side is 22 ft
    12·1 answer
  • Pls help fast, everything is in the attached file
    14·1 answer
  • Given f(x) = 5x - 3 , solve for when f(x) = 7
    5·2 answers
  • A group of friends wants to go to the amusement park. They have no more than $310 to spend on parking and admission. Parking is
    10·1 answer
  • I need help with these math problems, i’m not really good at math. i’m gonna be asking more questions cause i really need help w
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!