PreCalculus Problem Help?

rachel

I do not understand how to write this answer

The problem states

"Use the fact that sine is an odd function and cosine is an even function to show that tangent is an odd function."

-ms-christmas-

An odd function is symmetrical on the left and right side of the x axis. An even function is symmetrical.

Tangent is sine over cosine. One of the basic properties of even and odd functions is that the quotient of an even function and an odd function is an odd function.

Tangent is the quotient of an odd and an even function, so it's odd.

raj-k

"Use the fact that sine is an odd function and cosine is an even function to show that tangent is an odd function."

tanx=sinx/cosx

odd function implies

f(x) =−(fx)

even function implies

f(x) =f(−x)

sine is an odd function hence sin(−x)=−sinx

cosine is an even function hence cosx =cos(−x)

tan(−x) =sin(−x)/cos(−x) =−sin(x)/cos(x) =−tan(x)

Hence tangent is an odd function

christopher

tanx is the same as sinx/cosx and an odd function divided by an even function is an odd function