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

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Expert Answers

justaguide | Certified Educator

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.**

Student Comments

praveenm | Student

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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.