Question

Which of the six trigonometric functions are not defined at 0?

Answer 1

Trigonometric functions tangent, cotangent, secant, and cosecant are not defined at 0 degrees due to division by zero.

Step-by-step explanation:

The trigonometric functions that are not defined at 0 degrees are tangent, cotangent, secant, and cosecant, because they involve division by zero in their ratios. In terms of right triangles, these functions are undefined at 0 degrees because the tangent and cotangent involve the length of the opposite side divided by the adjacent side (or vice versa), and at 0 degrees, the opposite side length is 0, leading to division by zero. Similarly, secant and cosecant are the reciprocals of cosine and sine respectively, and since cosine of 0 degrees is 1, and sine of 0 degrees is 0, the cosecant of 0 degrees would require division by zero, which is undefined.

Answer 2

Using trigonometry table :
Sine 0 = 0
Cosine 0 = 1
Tangent 0 = 0
Co-secant 0 = 1/sine 0
= 1/0
= undefined
Secant 0 = 1/cos 0
= 1/1
= 1
Cotangent 0 = 1/tan 0
= 1/0
= undefined