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3 years ago

What are sin 0 and cos 0 for each value of 0?

Mathematics

1 answer:

belka [17]3 years ago

4 0

Answer:

a. sin 300 = -∛3/2, cos 300 = 1/2

b. sin -225 = √2/2, cos -225 = √2/2

c. sin 5π/6 = 1/2, cos 5π/6 = -3√2

d. sin -4π/3 = √3/2, cos -4π/3 = -1/2

Step-by-step explanation:

See unit circle

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A circle has the order pairs (-1, 2) (0, 1) (-2, -1) what is the equation . Show your work.

olga55 [171]

We know that:

$(x-a)^2+(y-b)^2=r^2$

is an equation of a circle.

When we substitute x and y (from the pairs we have), we'll get a system of equations:

$\begin{cases}(-1-a)^2+(2-b)^2=r^2\\(0-a)^2+(1-b)^2=r^2\\(-2-a)^2+(-1-b)^2=r^2\end{cases}$

and all we have to do is solve it for a, b and r.

There will be:

$\begin{cases}(-1-a)^2+(2-b)^2=r^2\\(0-a)^2+(1-b)^2=r^2\\(-2-a)^2+(-1-b)^2=r^2\end{cases}\\\\\\
\begin{cases}1+2a+a^2+4-4b+b^2=r^2\\a^2+1-2b+b^2=r^2\\4+4a+a^2+1+2b+b^2=r^2\end{cases}\\\\\\
\begin{cases}a^2+b^2+2a-4b+5=r^2\\a^2+b^2-2b+1=r^2\\a^2+b^2+4a+2b+5=r^2\end{cases}\\\\\\
$

From equations (II) and (III) we have:

$\begin{cases}a^2+b^2-2b+1=r^2\\a^2+b^2+4a+2b+5=r^2\end{cases}\\--------------(-)\\\\a^2+b^2-2b+1-a^2-b^2-4a-2b-5=r^2-r^2\\\\-4a-4b-4=0\qquad|:(-4)\\\\\boxed{-a-b-1=0}$

and from (I) and (II):

$\begin{cases}a^2+b^2+2a-4b+5=r^2\\a^2+b^2-2b+1=r^2\end{cases}\\--------------(-)\\\\a^2+b^2+2a-4b+5-a^2-b^2+2b-1=r^2-r^2\\\\2a-2b+4=0\qquad|:2\\\\\boxed{a-b+2=0}$

Now we can easly calculate a and b:

$\begin{cases}-a-b-1=0\\a-b+2=0\end{cases}\\--------(+)\\\\-a-b-1+a-b+2=0+0\\\\-2b+1=0\\\\-2b=-1\qquad|:(-2)\\\\\boxed{b=\frac{1}{2}}\\\\\\\\a-b+2=0\\\\\\a-\dfrac{1}{2}+2=0\\\\\\a+\dfrac{3}{2}=0\\\\\\\boxed{a=-\frac{3}{2}}$

Finally we calculate $r^2$ :

$a^2+b^2-2b+1=r^2\\\\\\\left(-\dfrac{3}{2}\right)^2+\left(\dfrac{1}{2}\right)^2-2\cdot\dfrac{1}{2}+1=r^2\\\\\\\dfrac{9}{4}+\dfrac{1}{4}-1+1=r^2\\\\\\\dfrac{10}{4}=r^2\\\\\\\boxed{r^2=\frac{5}{2}}$

And the equation of the circle is:

$(x-a)^2+(y-b)^2=r^2\\\\\\\left(x-\left(-\dfrac{3}{2}\right)\right)^2+\left(y-\dfrac{1}{2}\right)^2=\dfrac{5}{2}\\\\\\\boxed{\left(x+\dfrac{3}{2}\right)^2+\left(y-\dfrac{1}{2}\right)^2=\dfrac{5}{2}}$

7 0

3 years ago

The equation for the cross section of a parabolic satellite television dish is y = 1/45 x2, measured in inches. How far is the f

patriot [66]

Answer:

11.25

Step-by-step explanation:

The equation for a parabola is:

y − k = 1/(4p) (x − h)²

where (h, k) is the vertex and p is the distance from the focus to the vertex.

1/(4p) = 1/45

4p = 45

p = 11.25

The distance from the vertex to the focus is 11.25 inches.

3 0

3 years ago

How many years older will you be 1.60 billion seconds from now? (Assume a 365-day year.)

docker41 [41]

There are 31,536,000 Seconds in one year

In order to find out how much older you get, you just needed to divide it :

1,600,000,000 / 31,536,000

= 50,73 years older

hope this helps

3 0

3 years ago

-p/3 - 8 = -3 I need the show work too

professor190 [17]

Answer:

-15

Step-by-step explanation:

-3+8-5. 5x3=15 and because it is -p it would be -15.

3 0

3 years ago

Find the volume of a sphere whose r is 20 inches

Svet_ta [14]

I think the answer is 33510.32in³

4 0

3 years ago