Question

If F(theta)=tan theta=3, find F(theta+pi)

Answer 1

To find F(theta+pi), we can use the periodicity of the tangent function. Since tan(theta) equals 3, F(theta+pi) will also equal 3.

Step-by-step explanation:

To find F(theta+pi), we can use the periodicity of the tangent function. Since tan(theta) equals 3, we can write theta as arctan(3). Adding pi to theta gives:

F(theta+pi) = tan(theta+pi) = tan(arctan(3) + pi)

Using the periodicity of the tangent function, we know that tan(x + pi) = tan(x). Therefore,

F(theta+pi) = tan(theta+pi) = tan(arctan(3) + pi) = tan(arctan(3)) = 3

Answer 2

The period of the tan function is π so (∅ + π) would yield the same value as ∅
F(∅ + π) = 3