Question

If cot 0 = tan 30° what is 0?

Answer 1

option C (60 degrees)

Explanation:

solution attached in the picture

Answer 2

If
`\(\cot \theta = \tan 30^\circ\)`, then
`\(\theta = 60^\circ\)` because their values are reciprocals, with
`\(\tan 30^\circ = (√(3))/(3)\), and \(\cot 60^\circ = √(3)\).`

The relationship between cotangent (cot) and tangent (tan) is reciprocal. Specifically,
`\(\cot \theta = (1)/(\tan \theta)\)`. Since
`\(\tan 30^\circ\)` is known, we can find
`\(\theta\)`.

Given
`\(\cot \theta = \tan 30^\circ\)`, substitute
`\(\tan 30^\circ = (√(3))/(3)\)` (commonly known value).

`\[ \cot \theta = (1)/((√(3))/(3)) = (3)/(√(3)) = √(3) \]`

The standard trigonometric ratio for
`\(\cot 60^\circ\)` is also
`\(√(3)\)`. Therefore,
`\(\theta = 60^\circ\).`