Hello. I don't understand how to find a point on the terminal angle when you are given a degree. Can anyone help?

Question

anonymous · Answer

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katara11111 · Answer

Hello :) 

I'm sorry but I am still confused I looked over that and did not see anything about a terminal angle and finding a point. 

Sorry!

katara11111 · Answer

Can someone please try to explain it to me?

phi · Answer

this might help http://www.khanacademy.org/math/trigonometry/basic-trigonometry/unit_circle_tut/v/unit-circle-definition-of-trig-functions-1

amistre64 · Answer

the ordered pair (r,$\theta$) represents how far you turn "$\theta$" by how far you move from the origin "r".

amistre64 · Answer

other than that, what is it that is confusing you about it?

katara11111 · Answer

What if I am not given r? In my book it asks for example " θ=45 degrees choose a point on the terminal side" It then gives the choices "(2,2) (1,(rad)3) ((rad)3, 1)"

I can not understand for the life of me why the answer is (2,2)

amistre64 · Answer

if we make a 45 degree angle with the positive x axis|dw:1372076097058:dw|
we produce a line thru the origin with a slope of tan(45) = 1

y = x

amistre64 · Answer

which one of the given points is on that line?

amistre64 · Answer

another way to look at it is:  tangent and slope are both defined by y/x  so they are the same thing.

which point has an inverse tangent of 45 degrees?

tan(a) = y/x

a = $tan^{-1}(2/2)$

a = $45^o$

katara11111 · Answer

wait so if I do tan-1 would that work with any example or just this one? 

Also what if it is a larger angle or a negative? 

But for another question basically I just graph and look?

amistre64 · Answer

the line produced by the angle will always have the basic form:  y = mx

since m = tan(a) = y/x ,  then filling in the line equation is a matter of taking the inverse tangent of a given point.

so yes, if you know how to graph the angle then you can determine any point along the line that is formed

amistre64 · Answer

if just given a degree, then replace m by tan

y = tan(45) x

y = 1x

katara11111 · Answer

y = tan (m)x ?

Then how do I know y and x? I think I am missing something simple. I'm sorry.

amistre64 · Answer

you determine y and x from given options.

the key is relating the trig function "tangent" to the definition of the slope of a line "m".

slope is defined as y/x

tangent is defined as y/x

lets use a 60 degree angle for an example, we want to determine the equation:

y = mx

y = tan(a) x

y = tan(60) x

y = sqrt(3)/1 x  this is the usual form of a line that everyone is fond of seeing.  now we can take any of the given points and test if they fit the line

does 2,2 fit?:  2 = sqrt(3) * 2 = 2sqrt(3)
                      since 2 does not equal 2sqrt(3)  this point is not a line of 60 
                      degrees


does 1, sqrt(3):  sqrt(3) = sqrt(3) * 1 = sqrt(3)
                      since sqrt(3) equals sqrt(3)  this point IS on a line of 60 
                      degrees.

amistre64 · Answer

the inverse tangent method would also suffice:

you are given that:  m = y/x
                     tan(45) = y/x
                            45 = tan^-1 (y/x)

test out the given points.  it might help to recall that a point is defined as (x,y)

katara11111 · Answer

so if I can plug it in equal to the y and it doesn't work then it isn't right. I'm going to try an example could you tell me if I did it correctly?

katara11111 · Answer

Thank you! I figured out! :)

amistre64 · Answer

yay!  :)    i think the site went down for a bit the last time ....