anonymous
  • anonymous
If sine of x equals square root of 2 over 2, what is cos(x) and tan(x)? Explain your steps in complete sentences.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@jamesr @Xaze @MoonMoonWolf @miszzkeriee @mathway @Michele_Laino @mickey1513
anonymous
  • 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
  • anonymous
Note, we are working on cos right now. We will do tan after cos.

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anonymous
  • anonymous
I tried but couldn't get it.
anonymous
  • anonymous
@Nixy
anonymous
  • anonymous
Ok, what did you get for x?
anonymous
  • anonymous
4
anonymous
  • anonymous
Ok, one sec
anonymous
  • anonymous
By the way, using complete sentences how would I explain the key features of the graph of the tangent function?
anonymous
  • 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
  • anonymous
x = pie2
anonymous
  • anonymous
Once you know how to solve the problem you should be able to explain.
anonymous
  • anonymous
\( \huge x = \sqrt{2} \)
anonymous
  • anonymous
Yeah
anonymous
  • 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
  • anonymous
Since we have found cos, what do you think tan x =? \( \huge \tan x = \frac{y}{x} \)
anonymous
  • anonymous
tan x would be pie2/4?
anonymous
  • anonymous
Tan x = \( \huge \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} \) but you need to divide this
anonymous
  • anonymous
Can you divide that?
anonymous
  • anonymous
Wouldn't it equal 1?
anonymous
  • anonymous
You are correct!!!!
anonymous
  • anonymous
tan x = 1
anonymous
  • anonymous
AYYYY
anonymous
  • anonymous
so for the final answer how would i explain
anonymous
  • anonymous
Just go over the steps that we went through here
anonymous
  • anonymous
ok
anonymous
  • anonymous
thank u
anonymous
  • anonymous
YW
anonymous
  • anonymous
but for this how would i explain
anonymous
  • anonymous
Using complete sentences, explain the key features of the graph of the tangent function.
anonymous
  • anonymous
Is that a separate question on your homework?
anonymous
  • anonymous
nah separate
anonymous
  • anonymous
It is separate ?
anonymous
  • anonymous
yes
anonymous
  • anonymous
Ok, you just need to explain the key feature of the tan when it comes to graphing.
anonymous
  • 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
  • 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
  • anonymous
Got it?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
Good job. It is a lot to take in but keep practicing and you will get it.
anonymous
  • anonymous
Thanks Nixy

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