Given sin^2 x = (1 - cos(2x))/2 Prove: sin(x/2) = plus/minus sqrt((1 - cos(x))/2) Prove Complete the steps of the proof
Answers
Answer:
1. half angle
2. x
Step-by-step explanation:
The missing parts of the proof is the variable x.
What are Trigonometric Functions?Trigonometric functions are those functions which are the ratio of the sides of a right angled triangle.
Given,
sin² (x) = [1 - cos (2x)] / 2
We have to prove sin ([tex]\frac{x}{2}[/tex]) = ± [tex]\sqrt{\frac{1-cos (x)}{2} }[/tex]
First, we have
sin² (x) = [1 - cos (2x)] / 2
Substituting x/2 in place of x, we get,
sin² (x/2) = [1 - cos (2x/2)] / 2
sin² (x/2) = [1 - cos (x)] / 2
sin² ([tex]\frac{x}{2}[/tex]) = [tex]{\frac{1-cos (x)}{2} }[/tex]
Taking square root on both sides,
sin ([tex]\frac{x}{2}[/tex]) = ± [tex]\sqrt{\frac{1-cos (x)}{2} }[/tex]
Hence it is proved.
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Related Questions
(this is a practice question)
Answers
Answer:
<GHI = 135 degrees
Step-by-step explanation:
(3x + 12) + (x + 4) = 180
4x + 16 = 180
4x + 16 - 16 = 4x
180 - 16 = 164
4x = 164
4x / 4 = x
164 / 4 = 41
x = 41
3 * 41 + 12
3 * 41 = 123
123 + 12 = 135
A rocket is fired directly upwards with a velocity of 80 ft/sec. The equation for its height, H, as a function of time, t, is
given by the function
H (t) = -1612 + 80+
Find the time at which the rocket reaches its maximum height, and its maximum height.
5
a) O time =
22
sec, max height = 200 ft
b) O time = 80 sec, max height = 100 ft
5
c) O time =
2
sec, max height = 100 ft
d) O time = 5 sec, max height = 200 ft
5
e) Otime = sec, max height = 400 ft
23
Revie
Answers
Answer:
(c).
Step-by-step explanation:
h(t) = - 16 t² + 80 t
Coordinates of the vertex are:
t = - [tex]\frac{80}{2(-16)}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5 sec.
h = - 16(2.5)² + 80(2.5) = - 100 + 200 = 100 ft.
A coin is tossed 4 times. Find the probability that a maximum of one head (exactly one head or no head) turns up.
(A) 0.375 (B) 0.25 (C) 0.50 (D) 0.0625 (E) 0.3125
Answers
I would go with answer D
Every flip is a 50/50 so ever 2 would be .25 then multiply that by 2 for 4 flips and it gives you 0.0625
Find the area of the parallelogram. Round to the nearest hundredth if necessary.
6 m
8 m
cm2
Area =
Answers
The area of the parallelogram willl be equal to 48 square meters.
What is an area?
The space occupied by any two-dimensional figure in a plane is called the area. The parallelogram occupied by the parallelogram in a two-dimensional plane is called as the area of the parallelogram .
Given that:-
Height = 6 mBase = 8 mThe area will be calculated as:-
Area = Height x Base
Area = 6 x 8
Area = 48 square meters.
Therefore the area of the parallelogram willl be equal to 48 square meters.
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A quarter falls off a building that is 144
feet tall. If the equation for height as a
function of time is
h(t) = -16t2 + initial height where t is
time in seconds and h(t) is height in
feet, how many seconds will it take for
the quarter to hit the ground?
Answers
Answer:
3 seconds
Step-by-step explanation:
Initial height = 144 feet
t = Time taken
The equation of the height from the ground is
[tex]h(t)=-16t^2+\text{Initial height}[/tex]
The time taken to reach the ground is needed. Here the ground is taken as reference so [tex]h(t)=0[/tex]
[tex]0=-16t^2+144\\\Rightarrow -144=-16t^2\\\Rightarrow t=\sqrt{\dfrac{144}{16}}\\\Rightarrow t=3\ \text{s}[/tex]
So, time taken by the quarter to reach the ground is 3 seconds.
What is the equation of the line that is perpendicular to y=-3x+1 that passes through the point (9,0)?
y=1/3x-3
y=-1/3x+3
y=3x+9
y=-3x+3
Answers
Answer:
Step-by-step explanation:
the correct answer of the question is y=x/3-3 b.c
m1.m2 = -1 But m1=-3
so -3.m2=-1
-3.m2/-3=-1/-3
m2=1/3 therefore
Y=1/3x-3
Helpppp!!!!!! I need this nowwwww
Answers
OMG?!?!?!!?! HELP!!!?!?!?! PLEASE !?!?!? Thanks to those who do :D <3
A pump can fill 1800KL tank in one hour. How long would it take to fill a 90 KL tank?
Answers
a map that created using a scale of 1 inch equals 3 miles shows a lake with an area of 18 square inches was a actual area of the lake
Answers
Answer:
Step-by-step explanation:
18in^2(3mi/in)^2
18in^2(9mi^2/in^2)
162 mi^2
if a state issued license plates using the scheme of one letter followed by five digits, how many plates could it use
Answers
Answer:
786240 different license plates.
Step-by-step explanation:
The required number of plates that can be used is 2,599,974.
Given that,
State-issued license plates use the scheme of one letter followed by five digits, how many plates could it used is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Maxium five-digit number = 99999
Total letters = 26
Number of plates = 26 × 99999 = 2,599,974
Thus, the required number of plates that can be used is 2,599,974.
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ASAP I WILL GIVE BRAINIEST IF ANSWERED ASAP!! PLEASE PLEASE HELP
Answers
Answer:
2x + 3 =84
Step-by-step explanation:
Answer:
2x + 3 = 84
Step-by-step explanation:
my points is going lower and lower and lower and lower until its zero
But i dont care.
Just answer my question in the picture above.
Answers
Answer:
c, a, b
...................
2. What is the solution to the inequality
--4x > 132? Show your work
Answers
Answer:
x < -33 ( mark me as the brainliest )
Step-by-step explanation:
1) -4x > 132
2) -4x/4 > 132/-4
3) x < -33
Match each fraction on the left with the corresponding percent on the right. Some options on the right will be used more than
once.
Answers
Answer:
no picture
Step-by-step explanation:
Deduce the minimum value of sinx+cosx and give the corresponding values of x, for x E [-360;360]
Answers
The minimum value of both sine and cosine is -1. However the angles that produce the minimum values are different, [tex]-\pi/2, \pi[/tex] for sine and cosine respectively.
The question is, can we find an angle for which the sum of sine and cosine of such angle is less than the sum of values at any other angle.
Here is a procedure, first take a derivative
[tex]\frac{d}{dx}(\sin x+\cos x)=\cos x -\sin x[/tex]
Then compute critical points of a derivative
[tex]\cos x-\sin x=0\implies x_1=\frac{\pi}{4},x_2=\frac{5\pi}{4}[/tex].
Then evaluate [tex]\sin x +\cos x[/tex] at [tex]x_1,x_2[/tex].
You will obtain global maxima and global minima [tex]\sqrt{2}, -\sqrt{2}[/tex] respectively.
The answer is [tex]-\sqrt{2}[/tex].
Hope this helps.
ONLY answer if you know! Which of the following will have a negative result? (1 point)
O-8-(-10)
O 12-14
07-(-3)
Answers
PLEASEEEEE SOMEBODY CAN YOU LOOK AT THE ATTACHMENTS ITS MATH IM OFFERING A 69 POINTS
Answers
I don't know sorry but I recommend using quizlet
55 people showed up on a party.There were 3 less women than men.how many men were there?
Answers
Answer:
52
Step-by-step explanation:
55 - 3 = 52
give me brainiest wink wink
Set up a system of equations. If w is the number of women and m is the number of men, we know that w+m=55, and that w=m-3. If you solve this, you get that m-3+m=55 → m=29.
Ellie worked 6 hours on Monday, 4.5 hours on Tuesday, 4 hours on Wednesday, 5.75 hours on Thursday, and 3 hours on Friday. If she is paid $10.18 per hour. Find her gross earnings for the week.
Answers
Answer:
⚠️DO NOT RELY ON ME⚠️ But, just by doing It in my head i think it's 236.685, but I don't really know just my thought process and mental math
Which is the solution to the inequality? 2 3/5 <b - 8/15
A. b<2 1/15
B. b>2 1/15
C. b<3 2/15
D. b>3 2/15
PLS NO CHEATING. I RLY NEED THIS. IF U DONT CHEAT I WILL MARK BRAINLIEST
Answers
Step-by-step explanation:
i think it's a b and answer my new question it's 100 point question I really need the answer pls help me
5a+12b+30c ; a=3, b=2, and c=1 evaluate the expression for the given value of the variable.
Answers
Answer:
69
Step-by-step explanation:
5a+12b+30c
5(3)+12(2)+30(1)
15+24+30
39+30
69
Hoped this helps!
HELP ASAP
The radius of a quarter circle is 1.4 millimeters. What is the quarter circle's area?
Answers
Answer:
A = 1.5386
Step-by-step explanation:
Quarter circle area formula:
A = (πr²)/4
A= (π1.4²)/4
A = (3.14*1.96)/4
A = (6.1544)/4
A = 1.5386
Find the area of the shape below.
Give your answer in terms of pi
6cm
8cm
32cm
The diagram is not drawn to scale.
Answers
9514 1404 393
Answer:
164π cm²
Step-by-step explanation:
The area of a circle is given by the formula ...
A = πr²
The radius (r) is half the diameter (d), so the area of a semicircle in terms of its diameter is ...
1/2A = (1/2)(π)(d/2)² = (π/8)d²
The given shape is the combination of three (3) semicircles. The smallest has a diameter of 6 cm; the middle-sized one has a diameter of (32 cm -6 cm -8 cm) = 18 cm. The largest has a diameter of 32 cm.
The total area will be ...
area of largest + area of middle-size - area of smallest
= (π/8)(32² +18² -6²) = (π/8)(1312) . . . . cm²
The area of the shape is 164π cm².
A rectangle has vertices at P (16,16), Q(16,-16), R(-16,-16) and S(-16,16). The origin is the center of dilation and the rule of a dilation is (x,y)→(1/4x, 1/4y) What is P' of the dilated image, PQ’R’S’?
Answers
Answer:
(4, 4)
Step-by-step explanation:
So you're trying to find what P' is, and P' would be the dilation of P. This means that you apply the rule (x, y) --> (1/4x, 1/4y) with the coordinate point (16, 16). This would be:
(16, 16) --> (1/4 * 16, 1/4 * 16) = (4, 4)
Is it a function yes or no
Answers
Answer:
no
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
(2+5x)9= combine like terms
Answers
Answer:
18+45x
Step-by-step explanation:
What is the inverse operation needed to isolate the variable 4 = p - 8
Answers
If you want I can explain it to you in the comments
Answer:
To do this you need to add both sides by 8. yw
Step-by-step explanation:
-3 + 8n = -5
what is n?
Answers
Answer:
-1/4
Step-by-step explanation:
the u.s. landfill contained a total of 200 million tons of trash how many more million tons of trash has been paper than Rubber and leather?
Answers
Answer:
9,160,000 tons
HELP PLEASE DUE IN 4 MINUTES