If sine of x equals square root of 2 over 2, what is cos(x) and tan(x)? Explain your steps in complete sentences.

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- anonymous

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- anonymous

Ok, we have
\( \huge \sin x = \frac{\sqrt{2}}{2}\)
So we know that \( \huge \sin \theta = \frac{y}{r}\)
\( \huge y = \sqrt{2}\)
r = radius
\( \huge r = 2\)
\( \huge \cos x = \frac{x}{r} \)
Since we already know what y equals and r, we can use the following formula to find x
\( \huge x^2 + y^2 = r^2 \)
\( \huge x^2 + \sqrt{2}^2 = 2^2 \)
\( \huge x^2 + \sqrt{2}^2 = 2^2 - \sqrt{2}^2 \)
\( \huge \sqrt{x^2} = \sqrt{2^2 - \sqrt{2}^2} \)
Can you finish solving for x ?

- anonymous

Note, we are working on cos right now. We will do tan after cos.

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## More answers

- anonymous

I tried but couldn't get it.

- anonymous

- anonymous

Ok, what did you get for x?

- anonymous

4

- anonymous

Ok, one sec

- anonymous

By the way, using complete sentences how would I explain the key features of the graph of the tangent function?

- anonymous

\( \huge \sqrt{x^2} = \sqrt{2^2 - \sqrt{2}^2} \)
\( \huge \sqrt{x^2} = x\)
\( \huge x = \sqrt{2^2 - \sqrt{2}^2} \)
\( \huge 2^2 = 4 \)
\( \huge \sqrt{2}^2 = \sqrt{4} = 2 \)
So now we have \( \huge x = \sqrt{4 - 2} \)
What is the value of x ?

- anonymous

x = pie2

- anonymous

Once you know how to solve the problem you should be able to explain.

- anonymous

\( \huge x = \sqrt{2} \)

- anonymous

Yeah

- anonymous

So, \( \huge \cos x = \frac{x}{r}\) since we know what x is and r, we have cos x = \( \huge \frac{\sqrt{2}}{2} \)

- anonymous

Since we have found cos, what do you think tan x =? \( \huge \tan x = \frac{y}{x} \)

- anonymous

tan x would be pie2/4?

- anonymous

Tan x = \( \huge \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} \) but you need to divide this

- anonymous

Can you divide that?

- anonymous

Wouldn't it equal 1?

- anonymous

You are correct!!!!

- anonymous

tan x = 1

- anonymous

AYYYY

- anonymous

so for the final answer how would i explain

- anonymous

Just go over the steps that we went through here

- anonymous

ok

- anonymous

thank u

- anonymous

YW

- anonymous

but for this how would i explain

- anonymous

Using complete sentences, explain the key features of the graph of the tangent function.

- anonymous

Is that a separate question on your homework?

- anonymous

nah separate

- anonymous

It is separate ?

- anonymous

yes

- anonymous

Ok, you just need to explain the key feature of the tan when it comes to graphing.

- anonymous

Look in your book. It should tell you step by step. For instance you will have asymptotes at odd multiples of \( \huge \frac{\pi}{2} \)

- anonymous

Here are the properties of the tan
The domain is the set of all real numbers except odd multiples of \( \huge \frac{\pi}{2} \)
The range is the set of all real numbers
The tangent function is an odd function, as the symmetry of the graph with respect to the origin indicates.
The tangent function is periodic with period pi
The x-intercepts are .....,-2pi, -pi, 0, pi, 2pi, 3pi, .....
Vertical asymptotes occur at x = odd multiples of \( \huge \frac{\pi}{2} \)

- anonymous

Got it?

- anonymous

Yes

- anonymous

Good job. It is a lot to take in but keep practicing and you will get it.

- anonymous

Thanks Nixy

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