Question

If sine of x equals 1 over 2, what is cos(x) and tan(x)? Explain your steps in complete sentences.

Answer 1

@mathmale

Answer 2

Written in more compact form, sin x = 1/2, or sin x = (1/2).

Answer 3

You might want to sketch this situation, showing the lengths of all 3 sides of a right triangle with angle x such that sin x = 1/2. Use the DRAW feature, below.

Answer 4

HMM ok so I got cos=-radical 3/2?

Answer 5

I have the answers, I just want you to check them:) because I know u have to go soon

Answer 6

Your cos=-radical 3/2 needs re-writing to be correct. You're discussing the cosine of an angle, but you don't show any angle (argument) here. Can you fix that?

Answer 7

um +radical 3/2?

Answer 8

No. Let's focus on the COSINE function. What is its argument? Go back to the original problem statement for a clue.

Answer 9

um to find cos and tan?

Answer 10

every trig function has an argument. we cannot write sin, cos, tan, etc., without arguments.
What I'm trying to tell you is that your cos cannot stand alone. You mean cos x.

Answer 11

Are you familiar with the word "argument" in this discussion?

Answer 12

no:(

Answer 13

you are working with trig functions. The "x" in cos x is your argument; another word for it would be "input" or "independent variable."

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Answer 14

ok:)

Answer 15

Your cos=-radical 3/2 must be re-written so that the cosine function has an argument. Please do that now.

Answer 16

y= cos=-radical 3/2?
We dont have to that for my teacher though

Answer 17

It's VERY important that you do this.

Again, give the cosine function an input OR argument OR independent variab le.

What you want to write here is cos x = something.

Answer 18

cos=-radical 3/2 becomes cos x = -radical 3/2.
You should write the right side as -(radical 3)/2; if you don't, "radical 3/2" is ambiguous.

Answer 19

So, you should end up with

cos x =-(radical 3)/2

Answer 20

Quiz: What does the "x" represent?

Answer 21

Thank you!

Answer 22

then tan(x) would be radical 3/3 right?

Answer 23

You're welcome. See you again!

Answer 24

Again, J, you have to enclose "radical 3" in parentheses. Try again.

Answer 25

no! Wait! Was I right about tan(x)??

Answer 26

Also, please remember to insert the "argument" x next to the function "tan"

Answer 27

(radical 3)/3?

Answer 28

Your tan(x) was and is just fine.

So, tan(x) = (radical 3)/3. Very good!

Answer 29

Thanks! I have one last question though?

Answer 30

Actually, J, tan (x) = (radical 3)/2. Go ahead with your last question.

Answer 31

Using complete sentences, explain the key features of the graph of the cosine function

Answer 32

Really? Are you sure? Before that, I got 1/(radical 3)

Answer 33

I'm wrong. You're right. ;) tan(x) = 1/(radical 3), which can be rewritten as (radical 3)/3. Sorry.

Answer 34

It's okay:)

Answer 35

u didn't answer my last one though...?

Answer 36

"Using complete sentences, explain the key features of the graph of the cosine function"
I'd be glad to comment on YOUR remarks. What are characteristics of the graph of the cosine function?

Answer 37

Can y ou draw the cosine function without reference to a book or to the Internet?

Answer 38

um it has minimums and maximums?

Answer 39

Yes, it does. So does the sine function. What else can you say about the graph of the cosine function? Draw it, if you haven't already.

Answer 40

so cosine have a period of 2pi?

Answer 41

Right. It also has repeated minima and repeated maxima, every 2Pi units along the x-axis. Anything else?

Answer 42

Is the cosine function even or odd? How do you know?

Answer 43

odd. And by guessing:o

Answer 44

Better bone up on "even" and "odd." The cosine function is EVEN. Note that the graph is symmetrical with respect to the y axis.

Answer 45

Ahh! i will do that:)

Answer 46

R u now OK? Moe questions?

Answer 47

Can we find 2 more facts about the cosine function?

Answer 48

What is the max value? What is the min. value? What is the domain? What is the range?
Because this function repeats itself (graph repeats itself), what is a classifier (name) for this and the sine and the tan functions?

Answer 49

the domain could be all real #

Answer 50

right, and the range?

Answer 51

If you're not sure of the meaning of "range," please look it up (as it pertains to math)

Answer 52

i know what it is, I jiust dont know what it could be

Answer 53

Define "range."

Answer 54

its like the output of the x values?

Answer 55

so, 3x^2+12x+16
x=-2
y=-4

Answer 56

The "range" of a function is an INTERVAL. What does INTERVAL mean in math, and what is the vertical INTERVAL pertaining to the cosine function?

Answer 57

idek:/

Answer 58

What is the minimum value of the cosine function?
the max value?

Answer 59

the maximum point it can be

Answer 60

y=1?

Answer 61

You mean "maximum value." Right. What is the minimum value the cos x function can have?

Answer 62

0

Answer 63

Actually, about half of the graph of the cosine function is below the x-axis; half is above it.
Write the interval, using square brackets [ ], that represents the range of the cosine function.

Answer 64

kk:)

Answer 65

how would i find the minimum of g(x)=2*sin(x-pi)?

Answer 66

Let's finish y = cos x first. What is the min. value? the max value?

To answer your question: the min value is -2...but that's a separate question.

Answer 67

alright! Sorry:(

Answer 68

The min. value of the cos function is -1; the max is +1. Be certain that you know why this is and can explain it.
Now use the numerals -1 and 1 to write the RANGE of the cos function.

Answer 69

y=x>-1?

Answer 70

That's an inequality. An interval looks like [a,b], (a,b], (a,b), etc.
"a" represents the minimum, "b" the max. WRite the interval defined by the end points -1 and 1.

Answer 71

i give up:(

Answer 72

Min is -1; Max is +1.
The range is the closed interval [-1,1].

Answer 73

Please make a list of any vocabulary words with which you're not familiar. We could go over that after you've tried looking them up in a dictionary or in your math book or online.

Answer 74

kk! I will do that:) Will u be on tomorrow at this time?

Answer 75

Can't promise; probably won't be here because of a planned out of town trip. But you can message me and I can respond when back.
I'd suggest you make a list of the questions you have and then try your best to find the answers before bringing up the questions with me. Best of luck to you. Bye for now!

Answer 76

byee<3 thanks for all the help:)

Answer 77

bye!