Question

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

Answer 1

@jamesr
@Xaze
@MoonMoonWolf
@miszzkeriee
@mathway
@Michele_Laino
@mickey1513

Answer 2

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 ?

Answer 3

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

Answer 4

I tried but couldn't get it.

Answer 5

@Nixy

Answer 6

Ok, what did you get for x?

Answer 7

4

Answer 8

Ok, one sec

Answer 9

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

Answer 10

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

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

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

\( \huge 2^2 = 4 \)

\( \huge \sqrt{2}^2 = \sqrt{4} = 2 \)

So now we have \( \huge x = \sqrt{4 - 2} \)

What is the value of x ?

Answer 11

x = pie2

Answer 12

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

Answer 13

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

Answer 14

Yeah

Answer 15

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

Answer 16

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

Answer 17

tan x would be pie2/4?

Answer 18

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

Answer 19

Can you divide that?

Answer 20

Wouldn't it equal 1?

Answer 21

You are correct!!!!

Answer 22

tan x = 1

Answer 23

AYYYY

Answer 24

so for the final answer how would i explain

Answer 25

Just go over the steps that we went through here

Answer 26

ok

Answer 27

thank u

Answer 28

YW

Answer 29

but for this how would i explain

Answer 30

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

Answer 31

Is that a separate question on your homework?

Answer 32

nah separate

Answer 33

It is separate ?

Answer 34

yes

Answer 35

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

Answer 36

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

Answer 37

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 \( \huge \frac{\pi}{2} \)

Answer 38

Got it?

Answer 39

Yes

Answer 40

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

Answer 41

Thanks Nixy