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.
Comments
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.
"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) =â(fx)
even function implies
f(x) =f(âx)
sine is an odd function hence sin(âx)=âsinx
cosine is an even function hence cosx =cos(âx)
tan(âx) =sin(âx)/cos(âx) =âsin(x)/cos(x) =âtan(x)
Hence tangent is an odd function
tanx is the same as sinx/cosx and an odd function divided by an even function is an odd function