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3 years ago

Use a calculator to find the angle measure to the nearest degree for sin-1 (0.7071).

Mathematics

2 answers:

wariber [46]3 years ago

5 0

$\\ \tt\hookrightarrow \theta=sin^{-1}(0.7071)$

Let's use calculator

$\\ \tt\hookrightarrow \theta=44.99°$

Fact about sine(sin)

$\\ \tt\hookrightarrow Sin\theta=\dfrac{Perpendicular}{Hypotenuse}$

Naddik [55]3 years ago

3 0

The answer is 45 degree

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Let's find the perimeter of the window.

The bottom side is $x$ . The left and right sides make $2y$ .
The perimeter of a circle is $2\pi r$ , so the perimeter of a semicircle must be $\pi r$ , The radius is $\frac{1}2x$ , so that gives $\frac{1}2\pi x$ for the curve. All of that is equal to 12.

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We only want to use one variable to create the area formula, so let's solve for $y$ .

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Now that we have a value for $y$ in terms of $x$ , we can find the area in terms of $x$ .

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The area of the semicircle is going to be $\frac{1}2\pi r^2$ .

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$A_{sc}=\frac{1}8\pi x^2$

Now let's add the areas of the rectangle and semicircle.

$A=A_r+A_{sc}$

$A=6x-\frac{1}2x^2-\frac{1}4\pi x^2+\frac{1}8\pi x^2$

$A=6x-\frac{1}2x^2-\frac{1}8\pi x^2$

If you wanted to factor out $\frac{1}8$ like you did, this would become

$\boxed{A(x)=\frac{1}8(48x=4x^2-\pi x^2)}$

Now what we want to do is find what $x$ is when $A$ is at its highest point, Once we have the value for $x$ we can also find the value for $y$ , of course.

Let's put our equation in the general form of a quadratic.

$A(x)=(-\frac{1}2-\frac{1}8\pi )x^2+6x$

Now we can use the vertex formula $x=\frac{-b}{2a}$ .
( $a$ and $b$ refer to $ax^2+bx+c$ .)

$x=\frac{-6}{2(-\frac{1}2-\frac{1}8\pi)}$

$x=\frac{-6}{-\frac{1}4\pi -1}$

$x=\frac{-24}{-\pi -4}$

$\boxed{x=\frac{24}{\pi +4}}$

Now let's plug that in for $y=6-\frac{1}2x-\frac{1}4\pi x$ .

Since our final answers are in decimal form and not exact form, we can make our lives a little easier here and just use $x\approx3.36059492$ .

$y\approx6-\frac{1}2(3.36059492)-\frac{1}4\pi(3.36059492)$

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 $\boxed{y\approx1.68029746191}$

Let's take our answers for $x$ and $y$ and round to 2 decimal places.

$\boxed{x\approx 3.36\ ft}$

$\boxed{y\approx 1.68\ ft}$

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3 years ago

I need help with this problem.

Phantasy [73]

Csc^2x-cot^2x=1

Here is why

csc^2x=1+cot^2x

so:
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