Find the value of sin20 × sin30 × sin40 × sin80.


Please I need answers...​

Answers

Answer 1

Answer:

3/16

Step-by-step explanation:

Prove that sin 20 ×sin40 × sin60 × sin80 = 3/16.

We have to prove sin 20 × sin40 × sin60 × sin80 = 3/16.

Consider LHS

sin 20 × sin 40 × sin60 × sin80

Sin Values

In trigonometry, the sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle. The sine function is used to find the unknown angle or sides of a right triangle.

We know the trigonometric values of sin function

Proof

Consider LHS

sin 20 × sin 40 × sin60 × sin80

= sin60 [sin20 × sin40 × sin80]

= √3/2[sin20 × sin(60 – 20) × sin(60 + 20)]

= √3/2[sin 3(20)/4]

= √3/2[sin 60/4]

= √3/2[√3/2 × 4]

= √3/2 × √3/8 =  3/16

∴ LHS = RHS

Hence proved

Find The Value Of Sin20 Sin30 Sin40 Sin80. Please I Need Answers...

Related Questions

27 + x = 42 what is the value of x

Answers

Answer: x = 15

Step-by-step explanation:

Given:

27 + x = 42

Subtract 27 from both sides of the equation:

x = 15

27 + x = 42

Subtract 27 from both sides:

X = 15

) Find the value of b for which 50y +150 is a factor of y3 – by2 +by+3b. ​

Answers

[tex]f(y) = y^3-by^2+by+3b\\\\\text{Since 50y+150 is a factor of f(y), }\\\\~~~~~f\left ( -\dfrac{150}{50}\right) = 0 \\\\\implies f(-3)=0 \\\\\implies (-3)^3 -b(-3)^2+b(-3)+3b =0\\\\\implies -27-9b-3b+3b=0\\\\\implies -27-9b =0\\\\\implies 9b = -27\\\\\implies b = -\dfrac{27}9\\\\\implies b = -3[/tex]

A cylinder has a highet of 20cm and a volume of 1004.8cm. Calculate the radius of the base of the cylinder

Answers

Answer:

radius = 4 cm

Step-by-step explanation:

r≈4cm

Using the formula

V=πr2h

Solving forr

r=V

πh=1004.8

π·20≈3.99899cm

If x²+ y²= 80 and xy = 12, find the value of (x - y)².​

Answers

[tex](x-y)^2\\\\=x^2+y^2 -2xy\\\\=80-2(12)\\\\=80-24\\\\=56[/tex]

We need to factorise (x−y) 2

We know the identity (a−b)2 =a2 −2ab+b2

Thus we have (x−y)2 =x2 −2xy+y2

angle 1- what degree

Answers

Answer:

22 degrees

Step-by-step explanation:

The two bottom sides have the same angle which is 79 and all the angles must add up to 180, so 79 plus 79 is 158 and 180 minus 158 is 22.

Hope this helps.

BTW it's my birthday

Answer:

25°

Step-by-step explanation:

Exterior angle property of triangle:

Exterior angle of a triangle equals the sum of oppositer interior angles.

∠1 + 79 = 104

Subtract 79 from both sides

        ∠1 = 104 - 79

        ∠1 = 25°

help me find Find m< G .

Answers

Answer:

∠G=110°

Step-by-step explanation:

The 4 interior angles of a kite add up to 360. 100+40=140. 360-140=220. E and G are the only angles left so we know together they must equal 220. And ∠E and ∠G are congruent angles beceause of kite rules. So, we divide by 2 to get how much angle E and G are individually.

20 points. A certain event may occur, but it is unlikely to occur.

Which statement about the probability of the event is true?


A. The probability is close to 0.

B. The probability is 0.

C. The probability is 1.

D. The probability is less than 0.

Answers

Answer:

A

Step-by-step explanation:

Close to 0 means there isn't a certain number, and there also isn't a certain answer for what the probability. While all of the others are alreaady stated, this is the only one that is not.

Can y’all figure out the answer for me please

Answers

True

Explanation

Because if you flipped triangle def to straight it is actually the same but different size and that’s the meaning of “~”

Answer:

Step-by-step explanation:

true

if angle BCA is 90° and angle EFD is 90°

and if C to A is 14, half of that is 7 which is what F to D is


A polynomial function has – 5+ 3t as a root. Which of the following must also be a root of the function?

Answers

a

Radical roots occur as conjugate pairs

Given - 5 + t is a root , then

- 5 - t is also a root → a

14,15,3,15,14,14,18,15,8 mean ,mode,median determine which measure of center best represenrs the data

Answers

Answer:

Mean: 12.9

Mode: 14,15

Median: 14

Step-by-step explanation:

Allowing 20% discount on the marked price if a watch, the value of the watch will be Rs. 2376. If the VAT of 10% is added, find its marked price.

Ans: Rs. 2700​

Answers

original price be x

x-0.2x=23760.8x=2376x=2970

VAT 10%

So new price is 10% less

2970-0.10(2970)2970-297Rs 2673≈2700

Help picture below problem 13

Answers

Answer:

it's obtuse angle...

mark me brainliest

= Obtuse triangle

Explanation:

 (a triangle in which one of the interior angles measures more than 90° degrees.)

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER

Answers

Ok I see it

Angle MKP is 95° because
120-25= 95
And it’s obtuse because 95 is greater than 90

Hope this helps :)

‼️GET BRANLIEST HERE‼️






PLS AND TY IT IS DUE SOON :))​

Answers

Answer:

b = 0.62

Step-by-step explanation:

Hello!

We can look at the y-values of the function to find our multiplier. A multiplier will determine if the graph decays or grows in an exponential function, and by how much.

When x is 0, we can see the y-value is around 3, but as x approaches 1, the y-value comes to around 2.

We can find the multiplier by dividing the current term by the previous term.

2 ÷ 32/30.6666...

This number is closest to 0.62, so the approximation is 0.62.

2/3

0.6666..

Approximation is 0.62 (b)

Hope this helped! Stay healthy!

MAX POINTS PLEASE HELP Will make Brainliest

What is the period and frequency of the function graphed and how would the equation be written

Answers

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

The required equation is :

[tex]\qquad \sf  \dashrightarrow \:a \cos(bx) + k[/tex]

Now, let's find the required values :

period (p) = 6

[distance between any successive Crest or trough]

a = - 4 (flipped)

b = 2π/p = 2π/6 = π/3

k = -2

Distance of starting position from origin = k

Now, plug in the values ~

[tex]\qquad \sf  \dashrightarrow \: - 4 \cos( \frac{ \pi}{3}x ) - 2[/tex]

how would the equation be written with an amplitude of 3 maximum of 4 minimum of -2 period of 4 and midline of 1 (Will report scams)

Answers

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Here we go ~

The required equation is :

[tex] \qquad \sf \dashrightarrow\: y = asin(bx) +k [/tex]

Now, let's find the required values :

period (p) = 4

[distance between any successive Crest or trough]

a = - 3 (flipped)

b = 2π/p = 2π/4 = π/2

k = 1

Distance of starting position from origin = k

Now, plug in the values ~

[tex] \qquad\dashrightarrow \sf\: y = -3sin(\frac{\pi}{2}x)+1 [/tex]

Which shapes show equivalent fractions?

A.shapes A and B
B.shapes A and D
C.shapes B and C
D.shapes A, B, and D

Answers

Answer:

B.shapes A and D

Step-by-step explanation:

Cuz if u see very carefully u will see they are cubes (except b) and A and D had one of its side's covered so the answer is simply A and D

Write an equation of the line in slope-intercept form.
y=

Answers

Answer:

The equation of the line in slope intercept form is y=1/3x+2

Step-by-step explanation:

The points (4,7) and (r. – 5) lie on a line with slope – 3. Find the missing coordinate r ​

Answers

Answer:

[tex]r=\frac{14}{3}[/tex]

Step-by-step explanation:

Set up an equation and solve for r using the formula for slope:

[tex]\frac{5-7}{r-4}=-3\\ \\-2=-3(r-4)\\\\-2=-3r+12\\\\-14=-3r\\\\\frac{14}{3}=r[/tex]

which has a greater magnitude 17 ft above sea level or 11 ft

Answers

Answer:

1 - 52= 52 33= 33 52 > 33, so -52 dollars has the greater magnitude. 1 - 141 = 14 [23] = 23 14 < 23, so 23 feet has the greater magnitude.

Step-by-step explanation:

Hope This Helps

Find nth term of the sequence: 11, 15, 19, 23​

Answers

The term

tn=a+(n−1)d

Where a= first term and d= common difference

hope it helps...!!!

Your answer should be 43!

Help picture below problem 16

Answers

Answer:

Regular Hexagon

Step-by-step explanation:

There are six sides and all sides are equal

A haircut cost $16 which included tax. Joan tipped 20% and paid with a $50 bill. What was her change?

Answers

Answer:

32

Step-by-step explanation:

Answer: 30.8

Explanation: 20% of 16 is 3.2

16 + 3.2 = 19.2

50 - 19.2 = 30.8

I might be wrong but that's the answer I got

Find the area of the right triangle

Answers

Answer:

Formula for area of a triangle;

A = BH x 1/2

B = The base

H = The height

1/2 = Half of the product of (base x height)

We first need to figure out the base of this triangle, so count the units across from the base of this triangle.

The base is 4 units.

Now we need to find out the height, so count the units above starting from the base of this triangle and to the end of this triangle.

The height is 7 units.

Now plug these values into our equation:-

A = BH x 1/2

A = 4(7) x 1/2

A = 28 x 1/2

A = 28/2

A = 14, the area of this right triangle is 14 square units.

f(x) = - 0.05(x ^ 2 - 26x - 120)

What do the zeros of this function represent? Remember the zeros are where f(x) =0.​

Answers

We are given function  for the path coming out of the cannon.

We also given x is the horizontal distance from the cannon.

We need to explain, what f(x) represents there.

f(x) represents y-axis.

And y-axis also represents height.

Height represents a vertical distance.

Therefore, we could say f(x) represents vertical distance (height) from the cannon for x horizontal distance from the cannon.

22 mice were introduced to a new environment. Their population triples every year. Using m(t) as the function name and t for time, write this equation.​

Answers

Answer:

when were they introduced?

Step-by-step explanation:

How many minutes are in 3 hours?
There are 60 minutes in one hour.
Complete the table.

Answers

Answer:

180

Step-by-step explanation:

because there are 60 minutes in an hour and you need 3 you need to add 60 + 60 + 60 or your can do 60 x 3 which equals 180

Answer:

180 minutes

Step-by-step explanation:

1 hour - 60 minutes

2 hours - 120 minutes

3 hours - 180 minutes

Because there is 60 minutes in an hour, you can do 60 x 3 = 180. This will directly tell us how many minutes are in 3 hours. Or, you can add 60 minutes 3 times for 3 hours.

So, 60 x 3 = 180. There are 180 minutes in 3 hours.

A ball is thrown from an initial height of 3 feet with an initial upward velocity of 44 ft/s. The ball's height h (in feet) after seconds is given by the following.
h = 3+44t-16t^2

Find all values of t which the balls height is 23 feet.

Answers

Answer:

See below ↓↓

Step-by-step explanation:

Given function

h = 3 + 44t - 16t²

We need to calculate the possible values of t at h = 23 feet.

Subsituting h = 23,

23 = 3 + 44t - 16t²16t² - 44t + 20 = 0Divide throughout by 4 as it is a common factor4t² - 11t + 5 = 0

Solving for 't' using quadratic formula

t = 11 ± √121 - 4(4)(5) / 8t = 11 ± √41 / 8

Solutions

t = 11 + 6.4 / 8 = 17.4/8 = 2.175 secondst = 11 - 6.4 / 8 = 4.6/8 = 0.575 seconds

Answer:

t = 2.175 s (3 dp)

t = 0.575 s (3 dp)

Step-by-step explanation:

Given equation: [tex]h=3+44t-16t^2[/tex]

To find all values of t for which the ball's height is 23 ft, substitute h = 20 into the equation and solve for t:

[tex]\implies h=23[/tex]

[tex]\implies 3+44t-16t^2=23[/tex]

[tex]\implies 16t^2-44t-3+23=0[/tex]

[tex]\implies 16t^2-44t+20=0[/tex]

Factor out common term 4:

[tex]\implies 4(4t^2-11t+5)=0[/tex]

Divide both sides by 4:

[tex]\implies 4t^2-11t+5=0[/tex]

Quadratic formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]

Use the quadratic formula to solve for t:

[tex]\implies t=\dfrac{-(-11) \pm \sqrt{(-11)^2-4(4)(5)} }{2(4)}[/tex]

[tex]\implies t=\dfrac{11 \pm \sqrt{41}}{8}[/tex]

Therefore,

t = 2.175 s (3 dp)t = 0.575 s (3 dp)

Giving brainliest! need this question rlly soon thank you so much :)

Answers

u add BD which is 8, and AD with is 12 and BC=20
The answer is BC= 20

Question 1 – A two-mass (pulley) system begins in the initial configuration shown in the figure. Once this system is allowed to
move, the cart will move to the right and the suspended mass will fall with the same (magnitude of) acceleration. Determine this
acceleration, A, of this system, and the force in the cable, F, accurate to 3 sig. dig.
Assume the pulley and cable has no mass.

Answers

Answer:

the suspended mass will fall with the same (magnitude of) acceleration. Determine this

accelerat

Step-by-step explanation:

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