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

tan s = 0.2126

검증된 단계별 안내

Identify the given equation: \(\tan s = 0.2126\), where \(s\) is in the interval \([0, \frac{\pi}{2}]\).

Recall that to find \(s\), you need to use the inverse tangent function (also called arctangent), which is written as \(\arctan\) or \(\tan^{-1}\).

Apply the inverse tangent to both sides of the equation to isolate \(s\): \(s = \arctan(0.2126)\).

Use a calculator set to radians mode to find the approximate value of \(s\) by evaluating \(\arctan(0.2126)\).

Round the result to four decimal places to get the final approximate value of \(s\) within the interval \([0, \frac{\pi}{2}]\).

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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.

Understanding the Tangent Function

The tangent function relates an angle in a right triangle to the ratio of the opposite side over the adjacent side. It is periodic and defined for all angles except where cosine is zero. Knowing how to interpret tan s = 0.2126 helps in finding the angle s whose tangent value matches this ratio.

Inverse Tangent (Arctan) Function

The inverse tangent function, denoted arctan or tan⁻¹, is used to find the angle whose tangent is a given number. Since tan s = 0.2126, s = arctan(0.2126) gives the angle in radians. This function returns values typically in the interval (-π/2, π/2), which includes the given domain [0, π/2].

Radian Measure and Interval Constraints

Angles can be measured in radians, where π radians equal 180 degrees. The problem restricts s to the interval [0, π/2], meaning s is between 0 and 90 degrees. Understanding this interval ensures the correct solution is chosen, especially since tangent is positive and increasing in this range.

Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.tan s = 0.2126