Question
Express the following in terms of \( k \) if \( \tan (16)=k \) \( -\tan (376)-2 \)
Ask by Reyes Curry. in South Africa
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(-k - 2\)
Solution
Since \( \tan(376^\circ) \) can be simplified by using the periodicity of the tangent function, we note that
\[
\tan(376^\circ) = \tan(376^\circ - 360^\circ) = \tan(16^\circ)
\]
Given that \( \tan(16^\circ) = k \), we have
\[
\tan(376^\circ) = k
\]
Substituting this into the original expression,
\[
-\tan(376^\circ) - 2 = -k - 2
\]
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Simplify this solution Bonus Knowledge
To tackle this expression, we can start by simplifying \( \tan(376^\circ) \). We know that \( \tan(x) \) has a periodicity of \( 180^\circ \). So, we can reduce \( 376^\circ \) by subtracting \( 360^\circ \) (a full circle) to get \( 16^\circ \): \[ \tan(376^\circ) = \tan(376^\circ - 360^\circ) = \tan(16^\circ). \] Since \( \tan(16^\circ) = k \), we have \( \tan(376^\circ) = k \). Now, substituting this back into the expression we need to evaluate: \[ -\tan(376^\circ) - 2 = -k - 2. \] Thus, the expression in terms of \( k \) is: \[ -k - 2. \]
