QQuestionMathematics
QuestionMathematics
Rewrite the following as an equivalent algebraic expression. Assume x is positive. Make sure to use the ""/"" symbol in your answer to indicate division/fraction.
sec (cos- 1(x/ 6)) =
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Answer
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Step 1:: Recall the definition of the secant function and the inverse cosine function.
The inverse cosine function, often denoted as $$cos^{-1}$$ or $$arccos$$, returns the angle whose cosine is a given value.
Step 2:: Substitute the inverse cosine of x/ 6 for the argument of the secant function.
sec(cos^{-1}(x/6)) = rac{1}{cos(cos^{-1}(x/6))}
Step 3:: Use the definition of the secant function to simplify the expression.
Since $$sec(θ) = rac{1}{cos(θ)}$$, we have $$sec(cos^{-1}(x/6)) = rac{1}{x/6}$$.
Step 4:: Simplify the expression by dividing 1 by x/ 6.
To divide by a fraction, multiply by its reciprocal: $$ rac{1}{(x/6)} rac{1}{1} = rac{1}{x/6} rac{6}{1} = rac{6}{x}$$.
Final Answer
sec(cos^{- 1}(x/ 6)) = rac{6}{x}.
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