Find sinθ.
csc θ = -8/5

검증된 단계별 안내

Recall the definition of cosecant: \(\csc \theta = \frac{1}{\sin \theta}\). This means \(\sin \theta = \frac{1}{\csc \theta}\).

Substitute the given value of \(\csc \theta = -\frac{8}{5}\) into the equation: \(\sin \theta = \frac{1}{-\frac{8}{5}}\).

Simplify the fraction by multiplying numerator and denominator: \(\sin \theta = -\frac{5}{8}\).

Consider the sign of \(\sin \theta\) based on the quadrant where \(\theta\) lies. Since \(\csc \theta\) is negative, \(\sin \theta\) is also negative, which matches the simplified value.

Conclude that \(\sin \theta = -\frac{5}{8}\), consistent with the given \(\csc \theta\).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

도움이 되었나요?

주요 개념

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

Reciprocal Trigonometric Functions

The cosecant function (csc θ) is the reciprocal of the sine function (sin θ), meaning csc θ = 1/sin θ. To find sin θ when given csc θ, you take the reciprocal of the given value.

Sign of Trigonometric Functions in Quadrants

The sign of sine and cosecant depends on the quadrant where the angle θ lies. Since csc θ = -8/5 is negative, sin θ must also be negative, indicating θ is in either the third or fourth quadrant.

Simplifying and Interpreting Fractional Values

Given csc θ = -8/5, sin θ is the reciprocal, so sin θ = -5/8. Understanding how to simplify and interpret these fractional values is essential for accurate calculation and further problem-solving.

Find sinθ.csc θ = -8/5