Question

Solve the remaining equations for x, giving all solutions to the equation.

Sin x =3 and sin x= -1/2

Answer 1

First, if you're aware of the range for sin x, you can see that there are no solutions for sin x = 3. The range of the sin function is [-1, 1]. As for the second equation, there are going to be two values for -1/2. Since the sin function represents y-values, your two answerswill be in the 3rd and 4th quadrant. Do you know your unit circle okay enough to find the values for sin in those quadrants?

Answer 2

would the answers be 7pi/6 and 11pi/6?

Answer 3

Yep, absolutely ^_^

Answer 4

thank you so much!!

Answer 5

Sure, np.

Answer 6

For all solutions, wouldn't the answer be

\(x = \dfrac{7 \pi}{6} + 2 \pi n\) and \(x = \dfrac{11 \pi}{6} + 2 \pi n\), for all interger n.

Answer 7

what does the +2pin mean?

Answer 8

That means that the answer repeats itself every \(2\pi\) radians, or \(360^o\).
Remember that the sine function is cyclic.

Answer 9

oh okay that makes sense, thanks!