Which trigonometric ratio is undefined in value?

Question: Which trigonometric ratio is undefined in value?

Solution:
• sec 270° = 1/cos 270°
Since cos 270° = 0, we have 1/0​, which is undefined (∞).

• cosec 270° = 1/sin 270°
Since sin 270° = −1, we have 1/-1 = −1, which is defined.

• tan 0° = sin 0°/cos 0° = 0/1 = 0, which is defined.

• cot 90° = cos 90°/sin 90° = 0/1 = 0, which is defined.

Therefore, the trigonometric ratio that is undefined is sec 270°.