question 1-6 in $\\triangle jkl$, $m\\angle l = 90^\\circ$. if $\\sin j…

問題

question 1-6
in $\\triangle jkl$, $m\\angle l = 90^\\circ$. if $\\sin j = 0.6$, what is the value of $\\cos k$ to the nearest tenth?
enter the correct answer in the box.

解法ステップ

Understand the question
question 1-6
in $\\triangle jkl$, $m\\angle l = 90^\\circ$. if $\\sin j = 0.6$, what is the value of $\\cos k$ to the nearest tenth?
enter the correct answer in the box.
Explanation
Step1: Analyze the right triangle

In right triangle $ \triangle JKL $ with $ \angle L = 90^\circ $, the sum of the other two angles $ \angle J $ and $ \angle K $ is $ 90^\circ $ (since the sum of angles in a triangle is $ 180^\circ $, and $ \angle L = 90^\circ $). So $ \angle J + \angle K = 90^\circ $, which means $ \angle K = 90^\circ - \angle J $.

Step2: Use the co - function identity

We know the co - function identity $ \cos(90^\circ - \theta)=\sin\theta $. Let $ \theta=\angle J $, then $ \cos K=\cos(90^\circ - \angle J) $. By the co - function identity, $ \cos(90^\circ - \angle J)=\sin\angle J $.

Step3: Substitute the given value

We are given that $ \sin J = 0.6 $. Since $ \cos K=\sin J $, then $ \cos K = 0.6 $.
Final answer
$ 0.6 $

答え

Explanation

Step1: Analyze the right triangle

In right triangle $ \triangle JKL $ with $ \angle L = 90^\circ $, the sum of the other two angles $ \angle J $ and $ \angle K $ is $ 90^\circ $ (since the sum of angles in a triangle is $ 180^\circ $, and $ \angle L = 90^\circ $). So $ \angle J + \angle K = 90^\circ $, which means $ \angle K = 90^\circ - \angle J $.

Step2: Use the co - function identity

We know the co - function identity $ \cos(90^\circ - \theta)=\sin\theta $. Let $ \theta=\angle J $, then $ \cos K=\cos(90^\circ - \angle J) $. By the co - function identity, $ \cos(90^\circ - \angle J)=\sin\angle J $.

Step3: Substitute the given value

We are given that $ \sin J = 0.6 $. Since $ \cos K=\sin J $, then $ \cos K = 0.6 $.

Answer

$ 0.6 $

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Question Analysis

Subject mathematics

Sub Subject geometry

Education Level high school

Difficulty unspecified

Question Type calculation

Multi Question No

Question Count 1

Analysis Status completed

Analyzed At 2026-01-30T12:04:45

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question 1-6
in $\\triangle jkl$, $m\\angle l = 90^\\circ$. if $\\sin j = 0.6$, what is the value of $\\cos k$ to the nearest tenth?
enter the correct answer in the box.

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