derivation through first principle sin 2x?

Answers

Answer 1

9514 1404 393

Explanation:

Consider the attached diagram.

Arc RB is centered at O and has a radius of 1. Angle ROD is designated angle α. It is duplicated as angle DOB, meaning that OD is the perpendicular bisector of chord RB. Triangles DFB and RGD are congruent (by HA). They are similar to triangle RDO by AA similarity.

Now, we can use the definitions of sine and cosine to find some segment lengths. Since the circle is of radius 1, the length RD is sin(α). Then, in triangle RGD, the length DG is sin(α)·cos(α). As we said, BF is congruent to DG, so the length BH is 2·sin(α)·cos(α). Again, by the definition of sine, BH = sin(2α). So, we have ...

  sin(2α) = 2·sin(α)·cos(α) . . . . the desired relationship

Derivation Through First Principle Sin 2x?

Related Questions

Escribir la ecuación de la circunferencia de centro (3,4) y radio r = 2

Answers

(x-3)^2 + (y-4)^2 = 4

It's due in 30 minutes!!

Answers

Answer:

14 cups = 7 pints

144 cups = 36 quarts

Step-by-step explanation:

PLEASE HELP WILL GIVE BRAINLIEST AND MAX POINTS!!!
(-8) x [tex]\frac{2}{3}[/tex] =
(-8) x (- [tex]\frac{2}{3}[/tex])

-[tex]\frac{18}{3}[/tex] =

[tex]\frac{18}{-3}[/tex] =

[tex]\frac{-18}{-3}[/tex] =

Answers

[tex](-8)*\frac{2}{3} = -\frac{16}{3}[/tex]

[tex](-8)*(-\frac{2}{3} ) = \frac{16}{3}[/tex]

[tex]-\frac{18}{3} = -6[/tex]

[tex]\frac{-18}{-3} = 6[/tex]

8th term of 24,20,50/3

Answers

Answer: 6.698

Step-by-step explanation:

Answer:

6.698

Step-by-step explanation:

Have a good day :)

Question is the answer someone please help me!!!! ​

Answers

Answer:

Min = 3

Max = 11

First Quartile = 6

Median = 7

Third Quartile = 9

Step-by-step explanation:

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Answer:

Your welcome

Step-by-step explanation:

PLZ HELP ME WILL MARK BRAINLIST AND 50 points IF THE ANSWER IS CORRECT!!!

Answers

Answer for the question:

It is B.

Use the intermediate value theorem to find the value of c such that f(c) = M. f(x) = x^2 - x + 1 text( on ) [1,8]; M = 21 c =

Answers

Answer:

[tex]c = 5[/tex]

Step-by-step explanation:

Given

[tex]f(c) = M[/tex]

[tex]f(x) = x^2 - x + 1[/tex]

[tex]Interval: [1,8][/tex]

[tex]M = 21[/tex]

Required

Find c using Intermediate Value theorem

First, check if the value of M is within the given range:

[tex]f(x) = x^2 - x + 1[/tex]

[tex]f(1) = 1^2 - 1 + 1[/tex]

[tex]f(1) = 1[/tex]

[tex]f(x) = 8^2 - 8 + 1[/tex]

[tex]f(x) = 57[/tex]

[tex]1 \le M \le 57[/tex]

[tex]1 \le 21 \le 57[/tex]

M is within range.

Solving further:

We have:

[tex]f(c) = f(x) = M[/tex]

[tex]f(x) = 21[/tex]

Substitute 21 for f(x) in [tex]f(x) = x^2 - x + 1[/tex]

[tex]21 = x^2 - x + 1[/tex]

Express as quadratic function

[tex]x^2 - x + 1 - 21 = 0[/tex]

[tex]x^2 - x - 20 = 0[/tex]

Expand

[tex]x^2 + 4x - 5x - 20[/tex]

[tex]x(x+4)-5(x+4)=0[/tex]

[tex](x - 5)(x+4) = 0[/tex]

[tex]x - 5 = 0[/tex] or [tex]x + 4= 0[/tex]

[tex]x = 5[/tex] or [tex]x = -4[/tex]

The value of [tex]x = -4[/tex] is outside the [tex]Interval: [1,8][/tex]

So:

[tex]x = 5[/tex]

[tex]f(c) = f(x) = M[/tex]

[tex]f(c) = f(5) = 21[/tex]

By comparison:

[tex]c = 5[/tex]

Angle x and Angle y are vertical angles. Angle x is 157 degrees. What is the measure of Angle y?

Answers

Answer: 157 degrees

Step-by-step explanation: Since vertical angles have the same measure and we're given that the measure of angle x is 157 degrees, then we know that the measure of angle y is also 157 degrees.

lus
Payton thought the mix would make 36
cookies, but it only made 28. What was
her percent error?
Round to the nearest percent .

Answers

Answer:Percent error=29%

Step-by-step explanation:

Percent error=(Estimated value-Actual value/ Actual value) × 100

Estimated value = amount of cookies Payton thought the mix could make = 36

Actual Value= Amount of cookies made= 28

Percent error= (36- 28)/ 28 x 100

=8/28 x 100

=0.2857 x 100

=28.57 rounded to 29%

-3(x - 1) + 9 = 15 find the varible

Answers

Answer:

x = -1

Step-by-step explanation:

-3(x-1) + 9 = 15

-3x + 3 + 9 = 15

-3x = 3

x = -1

Answer:

The variable (x) is -1.

Step-by-step explanation:

use the distributive property

-3(x - 1) + 9 = 15

-3x + 3 + 9 = 15

-3x + 12 = 15

       -12    -12

-3x = 3

divide by -3

x = -1

F(x)=-x2-7x-5
Find f(-5)

Answers

Answer:

f(-5)=5

Step-by-step explanation:

the "-5" is telling us what to plug in for x. So, the new equation would be:

f(-5)= -(-5)^2-7(-5)-5

if we reduce, the expression would be

-25+35-5

our final answer would be 5.

2/3x=1/3 whats the awnser

Answers

Answer:

1/2

Step-by-step explanation:

I think so im not sure tho so sorry if its incorrect

Answer: x=1/2 is going to be your answer for this problem.

Match each percent with the fraction or decimal equivalent

Answers

25% - 0.25
15% - 3/20
6.5% - 0.065
5% - 1/20
7% - 0.07

Givin
m∠1 + m∠2 = m∠3 + m∠2

Reason
?​

Answers

Answer:

m∠1 + m∠2 = m∠3 + m∠2= you

np UwU

What integer does the arrow indicate?



-9
-14
-3
6

Answers

Answer:

-9

Step-by-step explanation:

The arrow points to an negative number

The arrow points to -9

Answer:

-9

Step-by-step explanation:

-9)llkjsjsjdjdjsjjwjaksk

What is eight hundred seven thousand, eight hundred twenty five in standard form?

Answers

so you should write 8 in a box then under the box write what place it is like hundredth and you do the same for the rest

8                                       0               7           , 8              2           5

hundred thousandth^  and so on^

Triangle with base 21 in and height 14in

Answers

Answer:

A = (1/2)bh

Step-by-step explanation:

A = (.5)(21)(14)

can someone help me with this?​

Answers

Answer:

p + 10

Step-by-step explanation:

We have an expression

"10 more than the number p"

How will you write the phrase?

The expression "10 more than the number p" shows that whatever amount p is, the total will always be 10 more of value than p. Therefore some type of adding is supposed to be here. Since this unknown value of a number will always be 10 more than p, we can come up to assume that p will be added by 10.

p + 10

All sneakers at Footlocker are 25% off. Mark wants to buy a $95 pair of Jordan's. How much will he have to pay for the Jordan's?

Answers

He will have to pay 70$

lus
Solve for x.
x = [?]
2x+16,
4x - 16
Enter

Answers

Answer:

i got x= 16/165

Step-by-step explanation:

What is the Surface Area of this Prism?

Answers

Total surface area:

792 in^2

Help

Don’t use for points or will be reported and take the points back

Answers

Answer:

A

Step-by-step explanation:

bc thats the one that makes more sense to me

Answer:

A

Step-by-step explanation:

It’s a, because equiangular triangle means having an equal angles

Anita knits 7 centimeter s of scarf each night. How many nights will Anita have to spend knitting in order to knit a total of 42 centimeters of scarf?

Answers

42 cm / 7 cm per night = 6 nights

Good luck to you!

13 subtracted from a number x

would u write it as 13-x sorry im not that smart

Answers

Answer:

[tex]x-13[/tex]

Step-by-step explanation:

Answer:

Are you cheating on your test like other 100,000 ppl? it is x - 13

Step-by-step explanation:

E

cos(44-A). cos(44+A) + cos (46 -A).cos(46 +A) = cos2A​

Answers

Answer:

-0.0777026243 A^5

Step-by-step explanation:

8x - 142 = 111 - 3x

Answers

Letter side Number side
8x-142= 111-3x
11x=253
x= 23

X=23

Answer:

23

ch ch ch f good first off

Please solve this thank you :)

Answers

Answer:

Scale= 3 x=9 y=15

Step-by-step explanation:

Ms. Grant’s car gets between 20 and 22 miles per gallon, inclusive. The gasoline she uses costs between $4.20 and $4.50 per gallon, inclusive. What is the greatest amount Ms. Grant will spend on gasoline to drive her car 200 miles

Answers

Answer:

You need to be more clearer with the money amount not like 4.20 - 4.50

Step-by-step explanation:

Mrs. Rossi's vegetable garden is 11 Ft long and 8 ft wide, next to her flower garden, which is 6 ft by 5 ft. How many square feet of garden does Mrs. Rossi have in all?

Answers

Answer:

118ft²

Step-by-step explanation:

11 × 8 = 88

6 × 5 = 30

88 + 30 = 118

good luck, i hope this helps :)

Please help
The slope of a line determines the direction the line is traveling from left to right.
True o false?

Answers

The answer of this is true

Answer:

True

Step-by-step explanation:

The slope both the steepness and the direction of the line

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