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2 years ago

Find cos theta if sin theta = 2/3. assume the terminal side of the angel falls in quadrant 2

1 answer:

3 0

Well knowing that the terminal arm of the standard position angle is in quadrant 2, we can determine the reference angle, in quadrant 2, by simply taking the difference between 180 and whatever the angle is.

So ø reference = 180 - ø in standard position.

Regardless, the reference angle is in quadrant 2, we need to then label the sides of the reference triangle based on the opposite and hypotenuse.

Solve for adjacent side using Pythagoras theorem.

A^2 = C^2 - B^2
A^2 = 3^2 - 2^2
A^2 = 9 - 4
A^2 =5
A = sq root of 5.

Then write the cos ratio using the new side.

Cos ø =✔️5/3. Place a negative in front of cos ø as cos is negative in second quadrant.

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Function f is an exponential function. It predicts the value of a famous painting, in thousands of dollars, as a function of the

nalin [4]

Answer:

$y=8 \cdot (\frac{5}{4})^x$

$f(x)=8 \cdot (\frac{5}{4})^x$

$f(x)=8 \cdot (1.25)^x$

Step-by-step explanation:

We are going to see if the exponential curve is of the form:

$y=a \cdot b^x$ , ( $b\neq 0$ ).

If you are given the $y-$ intercept, then $a$ is easy to find.

It is just the $y-$ coordinate of the $y-$ intercept is your value for $a$ .

(Why? The $y-$ intercept happens when $x=0$ . Replacing $x$ with 0 gives $y=a \cdot b^0=a \cdot 1=a$ . This says when $x=0 \text{ that} y=a$ .)

So $a=8$ .

So our function so far looks like this:

$y=8 \cdot b^x$

Now to find $b$ we need another point. We have two more points. So we will find $b$ using one of them and verify for our resulting equation works for the other.

Let's do this.

We are given $(1,10)$ is a point on our curve.

So when $x=1$ , $y=10$ .

$10=8 \cdot b^1$

$10=8 \cdot b$

Divide both sides by 8:

$\frac{10}{8}=b$

Reduce the fraction:

$\frac{5}{4}=b$

So the equation if it works out for the other point given is:

$y=8 \cdot (\frac{5}{4})^x$

Let's try it. So the last point given that we need to satisfy is $(2,12.5)$ .

This says when $x=2$ , $y=12.5$ .

Let's replace $x$ with 2 and see what we get for $y$ :

$y=8 \cdot (\frac{5}{4})^2$

$y=8 \cdot \frac{25}{16}$

$y=\frac{8}{16} \cdot 25$

$y=\frac{1}{2} \cdot 25}$

$y=\frac{25}{2}$

$y=12.5$

So we are good. We have found an equation satisfying all 3 points given.

The equation is $y=8 \cdot (\frac{5}{4})^x$ .

4 0

3 years ago

The value of the 4 in 34,258 and 47,163

Lera25 [3.4K]

The value of 4 in 34,258 is 10 times the value of the 4 in 47,163.

7 0

3 years ago

How would I write a square root symbol

enyata [817]

Answer:

$\sqrt{x}$ with x being square rooted.

6 0

3 years ago

Read 2 more answers

Solve for m. m + 4 3 = 2 what is m HELP MEEEEE!!!!!!!!!!!

Anna71 [15]

hi there user! Looks like your looking for help, so Mizuki came here to help you!

the answer is:

m is 2/3

The whole work I did:

m + 4 ÷ 3 = 2

m + 4/3 = 2

m + 4/3 - 4/3 = 2 - 4/3

m = 6/3 - 4/3

m = 2/3

Anyways hope this helped! qwq

7 0

2 years ago

Read 2 more answers

Much like sound bites of news stories, statistical studies are often reduced to one- or two-sentence "stat-bites." For thest

Ira Lisetskai [31]

Answer:

Step-by-step explanation:

Given that According to a video streaming service, 48% of American couples are "cheaters", that is—they promise each other to watch a filmtogether, but one of them first watches it alone.

Here if this is binomial with two outcomes we can easily say that the other 52% couples go together movies.

But here there are not only two outcomes.

The other possibilities are:

i) Either both do not go to movies

ii) Both cheat and go to movies separately

Thus since there are not exactly two outcomes, we cannot say the other 52% go to movies together.

As much as say that 52% of couples are not cheating in this way.

8 0

3 years ago