Question

For what x-value(s) does cos(x) = 0?

Answer 1

Hi Kailee...do you want a super easy way to always remember how to answers these questions?

Answer 2

sure?

Answer 3

ok...gimme sec to do a drawing for you...you will love it...one sec

Answer 4

sweet

Answer 5

all you have to do is sketch this simple unit circle, label your points at zero, 90, 180, 270 degress...then just follow the (cos,sin) convention! :o) super easy!

Answer 6

so the cos of 270 would be 0

Answer 7

or the sin of 270 would be -1...get it?

Answer 8

Oh, I see

Answer 9

So tangent would be what of this ?

Answer 10

yeah...so to answer your question...where is the cos equal to zero? well just look where your x corrdinate is zero, and that is your degree!

Answer 11

Where tangent would be 0

Answer 12

tangent of equal to zero would be obviously a sin/cos but only as long as you dont divide by zero...for example...at zero or 360 degrees, sin is 0 and cos is one, so tangent at zero or 360 degrees would be 0/1=0...so one point where the tangent equals zero would be at zero degree or 360 degrees

Answer 13

then just keep doing that for all your angles!

Answer 14

So, what about for y values?

Answer 15

Same or no?

Answer 16

try to rephrase your question...what about y values exactly?

Answer 17

What is the y-value for f(x) = tan(x) when x = 180°? to be specific

Answer 18

-1
180°
0
does not exist
those are my options

Answer 19

well think about it for a second...that basically is asking you what is the tangent at 180 degrees right? so look at your circle and find 180 degrees...then just look at the y coordinate

Answer 20

So -1?

Answer 21

obviously a y value isn't going to be a degree...it will be a specific coordinate...at 180 degrees, you only have 2 to choose from...so look at your picture and pic the number that corresponds to the cos point of (cos, sin)

Answer 22

yep...-1...use your calculator to confirm if you aren't sure as a double check!

Answer 23

and then I have What is the y-value for f(x) = tan(x) when x = -45°?

Answer 24

It doesnt make sense to me, because its -45....

Answer 25

ok...well to answer that question, you have to draw more lines through your unit circle, and label the points accordingly

Answer 26

do you know how to draw the entire unit circle using both radians and degrees?

Answer 27

No

Answer 28

ok...well in ordfer to survive trig and on into calculus, you MUST know how to do that in your sleep...have you even been taught about radians yet or are you just working in degrees?

Answer 29

just degrees

Answer 30

no problem...everyone starts out learning about degrees first...i can show you...its really easy....i am curious though...are you going past trig in the future and on into calc?

Answer 31

Yup

Answer 32

I'm only a freshman, ha.in high school

Answer 33

thats okay...if you want i can show you, but if i'm gonna put in this effort, you have to promise me to keep a copy of your unit circle! :o)

Answer 34

I will.

Answer 35

http://math.rice.edu/~pcmi/sphere/degrad.gif Wait, this?

Answer 36

kinda?

Answer 37

yeah...technically that is the unit circle but they should have labeled a few things differently and it's a bit crowded...how about you draw 2 unit circles...one for degrees, and one for radians...that way it isn't cluttered...as you go on past trig, you won't even use degrees anymore...all calculus stuff is done in radians...you ready?

Answer 38

ah, I guess so

Answer 39

i need to hear more enthusiasm than that!...i'm giving you a holy grail here! :o)

Answer 40

xD

Answer 41

ok...get a piece of paper and follow my lead...

Answer 42

Alright