Find the approximate value of s, to four decimal places, in the interval [0 , π/2] that makes each statement true.

sec s = 1.0806

검증된 단계별 안내

Recall the definition of the secant function: \(\sec s = \frac{1}{\cos s}\). This means that \(\cos s = \frac{1}{\sec s}\).

Substitute the given value of \(\sec s\) into the equation: \(\cos s = \frac{1}{1.0806}\).

Calculate the value of \(\cos s\) from the above expression (you can do this with a calculator, but do not finalize the answer here).

Use the inverse cosine function to find \(s\): \(s = \arccos(\cos s)\), where \(s\) is in the interval \([0, \frac{\pi}{2}]\).

Express the value of \(s\) in radians and round it to four decimal places as required.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Definition of Secant Function

The secant function, sec(θ), is the reciprocal of the cosine function, defined as sec(θ) = 1/cos(θ). Understanding this relationship allows you to convert the given secant value into a cosine value, which is often easier to work with when solving for the angle.

Inverse Trigonometric Functions

Inverse trigonometric functions, such as arccos, are used to find the angle corresponding to a given trigonometric value. After finding cos(s) from sec(s), applying arccos helps determine the angle s within the specified interval [0, π/2].

Domain and Range Restrictions

The problem restricts s to the interval [0, π/2], which corresponds to the first quadrant where cosine values are positive. This restriction ensures the solution is unique and helps in selecting the correct angle from the inverse cosine function.

Find the approximate value of s, to four decimal places, in the interval [0 , π/2] that makes each statement true.sec s = 1.0806