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If cot 0 = tan 30° what is 0?

If cot 0 = tan 30° what is 0?-example-1

2 Answers

3 votes

Answer

option C (60 degrees)

Explanation:

solution attached in the picture

User Paynestrike
by
7.2k points
2 votes

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,
\(\theta = 60^\circ\).

User Gabriel Caceres
by
6.9k points

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