Question

What is the period for the tangent function? (Answer in radians.)

Please explain answer. Thank you!

Answer 1

What is the definition of the tangent of an angle?

Answer 2

the natural tangent of the arc subtending or measuring the angle

Answer 3

The tangent is the ratio of the vertical side of that triangle over the horizontal side

Answer 4

or in other words tan(x) = sin(x) / cos(x)

Answer 5

THe radius there is 1, it is the unit circle

Answer 6

where is the tangent undefined on that circle?

Answer 7

Recall if you have a fraction with a zero in the denominator , it is undefined

Answer 8

Tan(x) = sin(x) / cos(x)

If cos(x) = 0, the tangent is undefined right?

Answer 9

yes

Answer 10

where on the circle, is the cosine zero

Answer 11

It will be where the x coordinate is zero, in other words, on the Y axis

Answer 12

the x coordinate on the unit circle is cos(theta)

Answer 13

ok I see now I had to look at the drawing