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Explain why the trigonometric equation 2sinθ - 5 = 0 fails to have solutions.

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acaputi | Student, Undergraduate | eNoter

Posted March 11, 2012 at 12:46 AM via web

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Explain why the trigonometric equation 2sinθ - 5 = 0 fails to have solutions.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 11, 2012 at 12:51 AM (Answer #1)

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The trigonometric equation `2*sin theta - 5 = 0` does not have any solutions.

This is due to the fact that the value of the sine of any angle `theta` lies in [-1, 1]

`2*sin theta - 5 = 0`

=> `2*sin theta = 5 `

=> `sin theta = 5/2`

=> `sin theta = 2.5`

2.5 does not lie in [-1, 1].

This is the reason why the equation `2*sin theta - 5 = 0` has no solution.

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praveenm | Student, Grade 11 | Honors

Posted March 11, 2012 at 4:28 PM (Answer #2)

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=>

=>

the value of any angle should lie in between -1 and 1.

here, 2.5 donnot lie in between -1 and 1.

so  the trigonometric equation 2sinθ - 5 = 0 do not have any solutions.

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