All categories

2 years ago

Use a half-angle identity to find the exact value of sinPi/8

Mathematics

2 answers:

Vlad1618 [11]2 years ago

6 0

Answer:

Step-by-step explanation:

hello :

look this solution :

stellarik [79]2 years ago

5 0

Answer:

sin(π/8) = (1/2)√(2-√2)

Step-by-step explanation:

Using the half-angle formula ...

$\sin{\dfrac{\theta}{2}}=\sqrt{\dfrac{1-\cos{\theta}}{2}}$

We can let θ = π/4 and simplify the result as follows:

$\sin{\dfrac{\pi}{8}}=\sqrt{\dfrac{1-\cos{(\pi/4)}}{2}}=\sqrt{\dfrac{1-\dfrac{\sqrt{2}}{2}}{2}}=\sqrt{\dfrac{2-\sqrt{2}}{4}}\\\\=\boxed{\dfrac{1}{2}\sqrt{2-\sqrt{2}}}}$

You might be interested in

If the maximum value of y=-3x² + mx + 10 is 37, find the values of m.

uysha [10]

Step-by-step explanation:

y = -3x² + mx + 10

dy/dx = -6x + m.

When dy/dx = 0, -6x + m = 0. => x = m/6.

We have y = -3(m/6)² + m(m/6) + 10 = 37.

=> -m²/12 + m²/6 = 27

=> -m² + 2m² = 324

=> m² = 324

=> m = 18 or m = -18.

5 0

2 years ago

Read 2 more answers

Please help with this Math Question...

Nataly [62]

Answer: A

Step-by-step explanation:

f(x) = x³ + 4x² + 7x + 6

possible rational roots are ±{1, 2, 3, 6}

Try x = -2

-2 | 1 4 7 6

| ↓ -2 -4 -6

1 2 3 0 ← remainder is 0 so x = -2 is a root ⇒ (x + 2) = 0

The factored polynomial x² + 2x + 3 = 0 is not factorable so use the quadratic formula to find the roots.

a=1, b=2, c=3

$x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}$

$x=\dfrac{-(2)\pm\sqrt{(2)^2-4(1)(3)} }{2(1)}$

$x=\dfrac{-2\pm\sqrt{4-12} }{2}$

$x=\dfrac{-2\pm\sqrt{-8} }{2}$

$x=\dfrac{-2\pm2i\sqrt{2}}{2}$

$x = -1 \pm i\sqrt{2}$

$x = -1 + i\sqrt{2}$ $x = -1 - i\sqrt{2}$

$x - (-1 + i\sqrt{2})=0$ $x - (-1 - i\sqrt{2})=0$

The factors are:

$(x - 2)[x - (-1 + i\sqrt{2})][x - (-1 - i\sqrt{2})]$

5 0

2 years ago

Solve for w, where w is a real number. √w+9=5

irga5000 [103]

If w is real then we need ignore negative sign and consider it as a mod value. So the answer will be 2

5 0

2 years ago

Assume that x is a positive acute angle. Given: sin x =28/53 Find: sin 2x

alexdok [17]

Answer:

its sophisticated but answer is 3

Step-by-step explanation:

you have to dive deep into it and research

4 0

2 years ago

Ares of a rectangular floor of your house is Ax+5x-2. if the length is x+2 units, find A

Snezhnost [94]

Answer:

A=4.

Step-by-step explanation:

Note: In the expression of area the first term should be $Ax^2$ .

It is given that area of a rectangular floor of your house is $Ax^2+5x-2$ and the length is $(x+2)$ units.

We know that, area of a rectangle is

$Area=length\times width$

Since length of the rectangle is $(x+2)$ , therefore $(x+2)$ is a factor of $Ax^2+5x-2$ and the value of $Ax^2+5x-2$ is 0 at x=-2.

$A(-2)^2+5(-2)-2=0$

$4A-10-2=0$

$4A-12=0$

$4A=12$

Divide both sides by 4.

$A=4$

Therefore, the value of A is 4.

7 0

2 years ago