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Question
If tan θ = `(-4)/3`, then sin θ is ______.
Options
`(-4)/5` but not `4/5`
`(-4)/5` or `4/5`
`4/5` but not `- 4/5`
None of these
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Solution
If tan θ = `(-4)/3`, then sin θ is `underline((-4)/5 or 4/5)`.
Explanation:
Since tan θ = `- 4/3` is negative, θ lies either in the second quadrant or in the fourth quadrant.
Thus sin θ = `4/5` if θ lies in the second quadrant or sin θ = `- 4/5`, if θ lies in the fourth quadrant.
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