Cotangent

Cotangent tells you the ratio of the adjacent side to the opposite side in a right triangle, so it measures how steep an angle is from a side-length point of view. Because tangent is opposite divided by adjacent, its reciprocal flips that ratio, giving cot\theta = adjacent/opposite = cos\theta/sin\theta. This is why cotangent becomes very large when the angle is small and close to 0°, and undefined when sin\theta = 0.

Use cotangent when a problem gives you an angle and the ratio of adjacent to opposite sides, or when you already know sine and cosine and want to convert between them. It also appears often in trigonometric identities, calculus, and solving right-triangle and coordinate-geometry problems.

• Reversing the ratio and using opposite/adjacent instead of adjacent/opposite
• Forgetting that cotangent is undefined when sin\theta = 0
• Mixing up cotangent with the tangent reciprocal but plugging in degrees/radians incorrectly