Identify which of the six trig functions are: even, odd, or neither?

Question

the six trig functions are: sin, cos, tan, csc, sec, & cot.

Thanks in advance to anyone who can help!!

Answer 1

Odd: Sin, tan, cot, cosec
Even: Cos, Sec

Answer 2

not sure i have ever heard this before, but i figure that byu the graphs of the functions, tan and cot are neither, sin is probably even and cos is probably odd, this is pretty much guessing here, but i'd say the csc is even and sec is odd, again just by thinkning about the graphs, i don;t remeber being told this.

Answer 3

A function f(x) is: even iff f(-x) = f)x), odd iff f(-x)= -f(x).

You can easily see from the graph that sin(-x) = - sin(x) and cos(-x) = cos(x). Thus, sin is odd and cos is even.

Those facts let you decide on the parity (evenness or oddness) of all the others. For example, tan(-x) = (sin(-x))/(cos(-x)) = -sin(x)/(cos(x) = -tan(x), so tan is odd.

Answer 4

you could tell if an inverse function is unusual or whether it symmetric regarding the y-axis. In different words f(x) = f(-x). The function is unusual if f(-x) = -f(x). and neither if it neither of those are real. i'm hoping this helped..