The graph shows the number of paintballs a machine launches, y, in x seconds:

Let , 4 ,− 7 be a point on the terminal side of θ . find the exact values of cos θ , csc θ , and tan θ .

Makovka662 [10]

Ok, you are given a point and you need to find the exact values for $cos \theta csc \theta & tan \theta$

First thing first. We need to see if we are working with a unit circle and find the radius.

How to tell if we are working with a unit circle?
We know $x^2 + y^2 = r^2$ is a circle.

We know that to find the radius we can use the following formula:
$r^2 = \sqrt{x^2 + y^2}$

If $r^2 = \sqrt{x^2 + y^2} = 1$ we are working with a unit circle.

Lets see if it = 1.
$r^2 = \sqrt{4^2 + -7^2}$
$r^2 = \sqrt{16 + 49}$
$r^2 = \sqrt{65}$

Square both sides now
$\sqrt{r^2} = \sqrt{\sqrt{65}}$
$r = \pm 65^{\frac{1}{4}}}$

Since we squared, we have a + and a - but we disregard the - because we do not have - radii
$r = 65^{\frac{1}{4}}}$
We can also say
$r = \sqrt[4]{65}$

Ok, since r does not equal 1, we are not working with a unit circle but we have found r, which is our radius.

Now that we know the value of r, which is $r = 65^{\frac{1}{4}}}$ , we need to look at the identities of cos, csc and tan.

The identities:
$cos \theta = \frac{x}{r}$
$csc \theta = \frac{1}{y}$
$tan \theta = \frac{y}{x}$

Now that we know their identities and know the radius of our circle, we can find the exact values of cos, csc and tan.

$cos \theta = \frac{x}{r} = \frac{4}{65^{\frac{1}{4}}}$
$csc \theta = \frac{1}{y} = \frac{1}{-7}$
$tan \theta = \frac{y}{x} = \frac{-7}{4}$

The exact values for cos, csc and tan given the point (4,-7) are:
$cos \theta = \frac{4}{65^{\frac{1}{4}}}$
$csc \theta = \frac{1}{-7}$
$tan \theta = \frac{-7}{4}$

4 0

3 years ago

Forty-five more than a number

Maslowich

Answer:

n+45

Step-by-step explanation:

Just name "a number" as n or any other variable

8 0

3 years ago

Read 2 more answers

Disadvantages of mathematical models are the model is a _________ of the real problem and does not include all _____ of the prob

Nonamiya [84]

Answer:

Disadvantages of mathematicsl models are given.

Step-by-step explanation:

Disadvances of mathematicsl models are the model is a limited or bounded cases which taken from huge number of situations by ignoring many unknown facts of the real problem and does not include all important parameters or trivial parameters for accuricy of the result of system dynamics which gives a better result of the problem. The model may also only work in certain major state variables and parameters which may effect largly on the whole system.

3 0

3 years ago

If f(x) = x^2 + 2x - 4 and g(x) = 3x + 1 Find f(g(x)) = ?

Ray Of Light [21]

Answer;

f (x) = 2x-4g (x) =x^2

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

. Which of the following is the correct algebraic representation of the translation below?

stepladder [879]

Answer:

D) (x+6, y+5)

Step-by-step explanation:

You can start with the top corner of triangle A

Then count up 5 units and right 6 units

Because you count vertically 5 units that means you're using the y-axis, And because you're counting up, than means the values are positive.

And because you count horizontally 6 units you're using the x-axis, And you are counting to the right so the values are positive.

Down vertically=Negative Y-axis Values. Up vertically=Positive Y-axis Values

Right horizontally=Positive X-axis values. Left horizontally=Negative X-axis Values

8 0

3 years ago