Question

Which trigonometric functions are undefined when

x=0?
a) Sine and cosine
b) Tangent and cotangent
c) Secant and cosecant
d) All trigonometric functions are defined at x=0.

Answer 1

Tangent and cotangent are the trigonometric functions undefined when x=0 as they involve division by zero, while sine and cosine are defined for x=0.

Step-by-step explanation:

The trigonometric functions that are undefined when x=0 are tangent and cotangent. This is because the tangent function (tan) is defined as the ratio of the opposite side to the adjacent side of a right triangle, and when x (the adjacent side) is zero, you would be dividing by zero, which is undefined. Similarly, the cotangent function (cot) is the reciprocal of the tangent or the ratio of the adjacent side to the opposite side, and with x being zero, it would also result in an undefined value.

Therefore, the correct answer to the question is b) Tangent and cotangent. Sine (sin) and cosine (cos) functions are defined even when x=0 because sin(0)=0 and cos(0)=1, according to the unit circle definition of these functions.