Question

Which expressions are equivalent to −tan⁡ θ?

There may be more than one correct answer. Select all that apply.

1/cotθ
−1/cotθ
1/cot(−θ)
−1/cot(−θ)
tan/ θ
tan/(−θ)

Answer 1

−1/cotθ

1/cot(−θ)

tan(−θ)

Explanation:

The tangent function is a the ratio for an angle defined as opposite / adjacent. A negative applied to −tan⁡ θ will give the opposite value. This is also true for the function when taken on a negative angle. tan(−θ) = −tan⁡ θ. This identity is also true for sin, sec, and cot. Recall that cotangent is the reciprocal of tangent and is defined as the ratio adjacent / opposite. Taking the reciprocal of cotangent will be the same as tangent. Using this information the following are equivalent:

1/cotθ

−1/cotθ ----> The reciprocal of Cot is Tan

1/cot(−θ) ----> The reciprocal of Cot is Tan and cot(−θ) = −cot⁡ θ.

−1/cot(−θ)

tan θ

tan(−θ)----> tan(−θ) = −tan⁡ θ