I am really having problems with a part of calculus, for example when they say cos210 degrees=what in radians?

Question

i am really confused. the thing about sin secant and tan being only in the first and fourth i dont get it. please can someone explain this whole thing to me i will appreciate it. also when they say tan^ -1 (-1) wat the h**l does this mean

Answer 1

cos210 cannot be in radians. 210 deg can be! it is 7pi/6.

Now on use corrct wording.

Answer 2

you are asking quite a few things here...a radian is another way to measure the angle in a circle...there are 360 degrees in a circle and 2 pi radians, so pi radians = 180 degrees

therefore 210 degrees = 7/6 pi radians

when you say "being in the first and fourth", i am guessing you mean quadrants on a graph...the first quadrant (or fourth of the circle) is from 0 to 90 degrees; the second from 90 to 180, the third from 180 to 270 and the fourth from 270 to 360

sin secant and tan are defined in all of these; the sin is positive in the first and second quadrants; tan is positive in the first and third, and secant is positive in the first and fourth...but I am not sure if this is what you are asking

the notation tan^-1 is read as either inverse tangent or "arc tangent"

let's say we write that tan(135)=-1

and someone asks you what is the angle whose tangent is -1?

the mathematical way of writing that is through the inverse or arc tan...

tan^-1(-1) means "the angle whose tangent is -1" (and in this case the answer is 135 degrees)

sin^-1(1/2) is the arcsin of 1/2 and means the angle whose sin is 1/2 (and the answer to that is 30 degrees)

hope this helps  

Answer 3

I don't understand what you are asking for most of your question but tan^-1 is the inverse function of tan which basically means it does the opposite of doing tan to a number. note: tan^-1 is also more correctly called arctan as tan^-1 can be confused with cot which equals 1/tan.

Answer 4

180° = PI in radians

so 210° = 210/180*PI in radians = 7/6*PI

tan^-1 mean the inverse of tan:

for example if tan(x) = y then tan^-1(y) would be x

so to get the result of tan^ -1 (-1), you should get the value of X where tan(X) = -1