Question

Solve the equation for exact solutions in the interval [0°,360°). Use an algebraic method. (cot 0-√3)(√2 sin 0+1)=0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The solution set is (Simplify your answers. Type an integer or a fraction. Use a comma to separate answers as needed. Do not include the degree symbol in your answer.) B. The solution is the empty set.

Answer 1

30,135,210,225

Explanation:

`( \cot( \alpha ) - √(3) )( √(2) \sin( \alpha ) + 1) = 0`

Set both equal to 0

`\cot( \alpha ) = √(3)`

`\alpha = 30`

Cot has a period of 180 degrees so the other value is

`\alpha = 210`

For the other factor,

`√(2) \sin( \alpha ) + 1 = 0`

`\sin( \alpha ) = - (1)/( √(2) )`

Rationalize the denominator

`\sin( \alpha ) = - ( √(2) )/(2)`

`\alpha = 135`

Sin is reflective about the origin so if we find the distance from the original alpha , we get our other

`\alpha = 225`

answer.

So our solution set is

30,135,210,225