Find the exact value of tan π/12.
Answers
[tex]\textit{Half-Angle Identities}\qquad tan\left(\cfrac{\theta}{2}\right)= \begin{cases} \pm \sqrt{\cfrac{1-cos(\theta)}{1+cos(\theta)}} \\\\ \cfrac{sin(\theta)}{1+cos(\theta)}~~\leftarrow \textit{let's use this one} \\\\ \cfrac{1-cos(\theta)}{sin(\theta)} \end{cases} \\\\\\ 2\cdot \cfrac{\pi }{12}\implies \cfrac{\pi }{6}~\hspace{10em} \cfrac{~~ \frac{\pi }{6}~~}{2}\implies \cfrac{\pi }{6}\cdot \cfrac{1}{2}\implies \cfrac{\pi }{12}[/tex]
so let's use the double of the angle in the half-angle identities, check the picture below for the cosine, sine pairs
[tex]tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{sin\left( \frac{\pi }{6} \right)}{1+cos\left( \frac{\pi }{6} \right)}\implies tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{~~ \frac{1}{2}~~}{1+\frac{\sqrt{3}}{2}}[/tex]
[tex]tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{~~ \frac{1}{2}~~}{~~\frac{2+\sqrt{3}}{2}~~}\implies tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{1}{2}\cdot \cfrac{2}{2+\sqrt{3}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{1}{2+\sqrt{3}}~\hfill[/tex]
Related Questions
A 6pint bucket of paint costs $28.44 what is the price per cup
Answers
Answer:
I think there answer is 4.74
Step-by-step explanation:
so you divide
[tex]6 \div 28.44 \: and \: you \: get \: answer[/tex]
Question
Which of the following angle measures are possible for a triangle to be classified as acute? Select all that apply.
Select all that apply:
45°, 34", 101°
122, 36, 22
75°, 61°, 44°
22°, 86°, 72
Answers
Answer:
45°, 75°, 61°, 44°, 22°, 86°
Step-by-step explanation:
They have to be angles less than 90°.
Answer:
(c) 75°, 61°, 44°
(d) 22°, 86°, 72
Step-by-step explanation:
The largest angle must be less than 90°, and the sum of angles must be 180°. These conditions are met by the lists of angles shown above.
During a chess match there are 15 pieces left on the board. the ratio of the white pieces to black pieces is 3 : 2 how many white pieces are on the white board?
Answers
==========================================================
Explanation:
The ratio 3:2 scales up to 3x:2x for some positive whole number x.
We have 3x white pieces, 2x black pieces, and 3x+2x = 5x pieces total. Set this equal to the 15 mentioned and solve for x.
5x = 15
5x/5 = 15/5
x = 3
Therefore, there are 3x = 3*3 = 9 white pieces and 2x = 2*3 = 6 black pieces, which gives 9+6 = 15 total. The ratio 9:6 reduces to 3:2 after dividing both parts by the GCF 3.
Simple interest ending balance $41,900 at 4% for 2 years?
Answers
The simple interest is $3352.
Step-by-step explanation:Using PRT/100, we can find the interest.
=> 41,900 x 4 x 2/100 => 419 x 4 x 2=> $3352Conclusion:Therefore, the simple interest is $3352.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Which function has a greater rate of change?
Answers
Answer:
Function A
Step-by-step explanation:
In function A as x increases by 1, y increases by 5.
In function B there is a slope of -4.5 which means as x increases by 1, y increases by -4.5.
Rate of change of 5 is greater than a rate of change of -4.5.
shirt original price is $100 and is now 50% off what is the discount price now
Answers
Answer:
$50.00 is the discount price
Find the values of sin, cosine, and tangent, for
Answers
sin=3/5
cos=4/5
tan=3/4
[tex]sin = \frac{opposite}{hypotenuse} = \frac{3}{5} = 0.6\\\\cos = \frac{adjacent}{hypotenuse} = \frac{4}{5} = 0.66666666666666666666666666666667\\\\tan = \frac{opposite}{adjacent} = \frac{3}{4} = 0.75\\\\hypotenuse = 5[/tex]
HOPE THIS HELPS :)
122 is what percent of 145?
Answers
Answer:
84.1379%
Step-by-step explanation:
122 / 145 = 0.841379
(0.841379)(100) = 84.1379%
Good night, can someone please help me?
Answers
I Think Operation A is write
II
Homework: Secti...
Question 2, 7.1.5
>
Find the critical value Za/2 that corresponds to the given confidence level.
95%
.....
za/2
(Round to two decimal places as needed.)
(
Answers
Answer:
2.17
Answer and Explanation:
The critical value of z for 97% confidence interval is 2.17, which is obtained by using a z score table, that is: {eq}P(-2.17 < Z <...
Find the circumference of a circle with a radius of 8 mm.
Answers
Answer:
C=50.27mm
Step-by-step explanation:
C=2πr=2·π·8≈50.26548mm
84/120 equivalent fraction
Answers
Answer:
7/10
this should work
Step-by-step explanation:
Examine the figure. What is the measure of angle b?
Answers
B = 180-31
B = 149
Answer: 149
LAST ATTEMPT MARKING AS BRAINLIEST!! ( write a rule to describe each transformation)
Answers
Answer:
See below
Step-by-step explanation:
Dilation is 1/2
U (2, 3) U' (1, 1.5)
V (1, -2) V' (0.5, -1)
Solve for x; x: 6 = 54: 162 A. 1 B. 2 C. 3 D. 4
find x
Answers
Answer:
x = 2
Step-by-step explanation:
x:6 = 54:162
What is 54 to 162?
162/54 = 3.
So x times 3 should equal 6.
6/3 = 2.
x = 2
Let's confirm,
2:6 = 54:162
:)
Answer:
8 - 10
8 + 10
Step-by-step explanation:
edmentum/plato
3] If the p.d.f., of the random variable X is given by
f(x)= K/sqrt x &0 otherwise
(c) P(|X| < 3)
(d) E(2X - 2)
(e) V(3X)
Answers
Answer:
PDF for a continuous random variable is given. Use the PDF to find (a) and the CDF.
Pls help i neeed to get my grade up badly
Answers
Step-by-step explanation:
12 - 1/2r = ( 13 - 3/2r ) - ( 1 - r )
r - 13/6 = ( 7r - 3/2 ) - ( 2/3 + 6r )
13r + 20 = ( 6r + 7 ) + ( 13 + 7r )
-12 + r = ( -8 - r ) + ( 2r - 4 )
URGENT PLEASE HELP simplify (3^8 / 3^5)^3
Answers
Which is the equation of a circle with a radius of 6 and a center of (3,-1)?
(x - 3)2 + (y+1)2 = 36
(x+3)2 + (y - 1)2 = 36
(x+3)2 + (y - 1)2 = 6
(x-3)2 + (y+ 1)2 = 6
Answers
Answer:
358
Step-by-step explanation:
576
pls answer pls plsplspls pls
Answers
πr²/2
22×7×7/7×2
77cm²
πr²/2×2
πr²
22/7×3.5×3.5
38.5cm²
77-38.5=38.5cm²
Express your answer in scientific notation. PLS HELP
Answers
3600-6.3-100= 3493.7
hope this helps!
LAST ATTEMPT MARKING AS BRAINLIEST!! (Graph the image of the figure using the dilation given)
Answers
Answer:
There ya go
Step-by-step explanation:
Tracy bought a can of yellow paint to use on the table and chairs in her backyard. She used 1.25 liters of paint on the chairs. She has less than 3 liters of paint left for the table.
Answers
The inequality that describes the given problem is x - 1.25 < 3.
The given parameters:
Number of paints used on the chair, = 1.25 LitersNumber of paints left for the table, less than 3 litersLet the number of liters in one can of yellow paint = x
The following inequality can be used to represent the liters of paint left for the table.
the liters of paint left = x - 1.25
The liters of paint left is less than 3 liters;
x - 1.25 < 3
Thus, the inequality that describes the given problem is x - 1.25 < 3.
The missing part of the question is below:
Write the inequality that describes the given problem
Learn more about word problem of inequality: https://brainly.com/question/1194852
A group of friends were working on a student film that had a budget of $1300. They used $546 of their budget on props. What percentage of their total budget did they spend on props?
Answers
546/1300 x 100 = 42%
Rebecca draws a graph of a real-world relationship that turns out to be a set of unconnected points. Can the relationship be linear? Can it be proportional? Complete the explanation of your reasoning.
Answers
Answer:
Step-by-step explanation:
the difference of 3 times a number and 18 is 39 what is the number
Answers
Answer: 39
(3*(19))-18 = 39
57-18 = 39 we have the correct answer
If answer is correct I will mark as brainliest.
which of the following expresses the possible number of positive real solutions for the polynomial equation shown below?
5x^3+x^2-7x+28=0
A. Zero
B. Two or Zero
C. One
D. Three or one
Answers
Answer:
No positive real solutions.So the answer is zero.
Step-by-step explanation:
For what value(s) of k is + 3 a factor of 3 + 5 2 + − 9
FAST FASTTTT
Answers
Answer:
56
Step-by-step explanation:
Find the center and radius of the circle with the equation: (x=5)2 +(4-2)3-25
Answers
Answer:
center = (5 ,-3) and radius = 5
Step-by-step explanation:
Kelly base 3328 cookies each year she bakes twice as many cookies in October then in the other much how many cookies does Kelly back in December
Answers
There are 12 months and twice the amount of cookies in one month is equal to an extra month. So do 3328/13=256.