All categories

3 years ago

Part II: Find the sine, cosine, and tangent ratios of <y

Mathematics

1 answer:

Lorico [155]3 years ago

6 0

Answer:

sin θ = 22.62°

cos θ = 22.62°

tan θ = 22.62°

Step-by-step explanation:

From the diagram above

Opposite = 5

Adjacent = 12

Hypotenuse = 13

a) sin θ = Opp/Hypotenuse

sin θ = 5/13

sin θ = 0.3846153846

arc sin 0.3846153846

= 22.619864948°

Approximately = 22.62°

b) cos θ = Adjacent/ Hypotenuse

θ = 12/13

= arccos(0.9230769230769231)

22.619864948°

Approximately = 22.62°

c) tan θ = Opposite/Adjacent

θ = 5/12

= arctan(0.4166666666666667)

= 22.619864948°

= 22.62°

You might be interested in

If 2y^2+2=x^2, then find d^2y/dx^2 at the point (-2, -1) in simplest form.

horrorfan [7]

Answer:

$\frac{d^2y}{dx^2}_{(-2, -1)}=\frac{1}{2}$

Step-by-step explanation:

We have the equation:

$2y^2+2=x^2$

And we want to find d²y/dx² at the point (-2, -1).

So, let's take the derivative of both sides with respect to x:

$\frac{d}{dx}[2y^2+2]=\frac{d}{dx}[x^2]$

On the left, let's implicitly differentiate:

$4y\frac{dy}{dx}=\frac{d}{dx}[x^2]$

Differentiate normally on the left:

$4y\frac{dy}{dx}=2x$

Solve for the first derivative. Divide both sides by 4y:

$\frac{dy}{dx}=\frac{x}{2y}$

Now, let's take the derivative of both sides again:

$\frac{d}{dx}[\frac{dy}{dx}]=\frac{d}{dx}[\frac{x}{2y}]$

We will need to use the quotient rule:

$\frac{d}{dx}[f/g]=\frac{f'g-fg'}{g^2}$

So:

$\frac{d^2y}{dx^2}=\frac{\frac{d}{dx}[(x)](2y)-x\frac{d}{dx}[(2y)]}{(2y)^2}$

Differentiate:

$\frac{d^2y}{dx^2}=\frac{(1)(2y)-x(2\frac{dy}{dx})}{4y^2}$

Simplify:

$\frac{d^2y}{dx^2}=\frac{2y-2x\frac{dy}{dx}}{4y^2}$

Substitute x/2y for dy/dx. This yields:

$\frac{d^2y}{dx^2}=\frac{2y-2x\frac{x}{2y}}{4y^2}$

Simplify:

$\frac{d^2y}{dx^2}=\frac{2y-\frac{2x^2}{2y}}{4y^2}$

Simplify. Multiply both the numerator and denominator by 2y. So:

$\frac{d^2y}{dx^2}=\frac{4y^2-2x^2}{8y^3}$

Reduce. Therefore, our second derivative is:

$\frac{d^2y}{dx^2}=\frac{2y^2-x^2}{4y^3}$

We want to find the second derivative at the point (-2, -1).

So, let's substitute -2 for x and -1 for y. This yields:

$\frac{d^2y}{dx^2}_{(-2, -1)}=\frac{2(-1)^2-(-2)^2}{4(-1)^3}$

Evaluate:

$\frac{d^2y}{dx^2}_{(-2, -1)}=\frac{2(1)-(4)}{4(-1)}$

Multiply:

$\frac{d^2y}{dx^2}_{(-2, -1)}=\frac{2-4}{-4}$

Subtract:

$\frac{d^2y}{dx^2}_{(-2, -1)}=\frac{-2}{-4}$

Reduce. So, our answer is:

$\frac{d^2y}{dx^2}_{(-2, -1)}=\frac{1}{2}$

And we're done!

7 0

4 years ago

Complete the generic rectangle (PLEASE HELP)

navik [9.2K]

I believe the area of the blank rectangle, the biggest one, is 2800. The whole rectangle all together is 3225.

Explanation:

Since the length of one of the rectangles is 70, the rectangle with an area of 210 will have a side length of 3. This means the rectangle with an area of 15 has a side length of 5. That means the rectangle with an area of 200 has a side length of 40. Therefore, the blank rectangle has an area of 2800, as it's 2 side lengths are 70 and 40.

4 0

3 years ago

-x+4y=4 -x+3y=1 is (8,3) a solution of the system?

svetoff [14.1K]

check by plugging into both equations

-8+4(3)=4

-8+12=4

4=4

-8+3(3)=1

-8+9=1

1=1

(8,3) is a solution of the system

7 0

3 years ago

How to solve number b

Mkey [24]

You're on the right track. If they generated 380 less than 2012, then in 2013 they generated 9782-380 = 9402.
They used 10472 in 2012, so 10472+390 = 10862 used in 2013. now subtract used from produced to see how much they had to buy...
10862-10472 = 390
They had to buy 390khW from the power company.

4 0

3 years ago

In 5 OR MORE SENTENCES, write a short story explaining the graph OR write about the key features of the graph.

rewona [7]

The graph illustrated is divided into three seperate sections namely A, B and C, the short story culled from the graph is described thus:

Rate of change or slope = (Rise/ Run)

Rise = y2 - y1
Run = x2 - x1

SECTION A:

Slope = (40 - 0) ÷ (20 - 0) = 40/20 = 2

Distance traveled = 50 meters

SECTION B :

This section gives an horizontal line, hence, the slope is 0.

Distance covered = 0 ; as there was no change in the distance over the period of time.

SECTION C:

Slope = (80 - 50) ÷ (70 - 60) = 30/10 = 3

The total distance traveled = 80 - 50 = 30 meters

The total distance and time spent traveling :

Total distance traveled = (50 + 30) = 80 meters

Total time spent = 70 seconds (time at the 80 meter mark)

Hence, the story.

Learn more : brainly.com/question/25309609

6 0

3 years ago

Part II: Find the sine, cosine, and tangent ratios of <y ​

Part II: Find the sine, cosine, and tangent ratios of <y