Why are trig functions called a function?

Answer 1

a function is when it passes the vertical line test meaning that if you were to draw a vertical line in the graph, the line would not touch it twice. it means that for every imput you only have one output. for example you can't have the points (2,3) and (2,4). a circle is not a function but the sin wave is and so the cos.

Answer 2

In it's most abstract sense, a function taking a set X to a set Y is a subset of the cartesean product X x Y (set of all ordered pairs (x,y) where x is in X and y is in Y) where the first entry uniquely determines the second. Notice the key word "uniquely." That means that if I choose an x, I can't get two values for f(x) (this is what it means to be "well-defined" and all functions must be well-defined). If you take X and Y to be the real numbers, then the condition of well-defined is equivalent to the vertical line test that someone else mentioned.

So that's what a function is in general. The trig functions are all real valued functions, which is to say that Y is the real numbers. X will depend on which of the trig functions you choose. If you choose sin(x) or cos(x) then X is the real numbers also. To see this is a function, you know that sin(x) and cos(x) assign real numbers determined by x, and they are unique because they pass the vertical line test. You can do similar work on the other trig functions, but you need to identify what X is in each case (the others will not be the real numbers). Does this make sense?

Answer 3

because trigonometric functions are functions.

a function isa way to relate the elements of one set to the elements on the other set, with the property that the elements of the 1st set get assigned only 1 element from the second set.

for example
square root is NOT a function, because sqr(4) = 2, -2.
while cube root is since, cuberoot(9)=3, etc etc

Answer 4

A function is a rule which takes certain values as input values and assigns to each input value exactly one output value.


f(x)=sin(x) is a function.

For all x values, you will find a result.
if x=0 then f(0)=sin0=0
if x=90 then f(90)=sin90=1
if x=30 then f(30)=sin 30=1/2

As you see, this is the definition of a function.