Solve the equation on the interval

[dwlniles]

Solve the equation on the interval 0 ? ? < 2pi
2 sin ? + 6 = 7

This is what I have done so far:

2 sin ? + 6 = 7
2 sin ? = 1
sin ? = 1/2

This is where I get stuck....

I know the interval of ? = pi/6, 5pi/6

I'm just not sure how how you figure that out? Where does the pi/6, 5pi/6 come from?

 

[DrSteve]

To get the first quadrant angle, look at a 30, 60 , 90 triangle and remember that sin x is opposite/hypotenuse.

Sine is also positive in the second quadrant. To get the second quadrant angle you take $\displaystyle \pi$ minus the first quadrant angle.

 

[galactus]

As an aside, may I show a silly mnemonic used to remember the quadrants where the trig functions are positive.

A Smart Trig Class.

Which corresponds to All Sine Tangent Cosine.