SOLUTION: Help please! Find all the solutions for x to the nearest 0.01 radian in the interval [0,2π] for the equation: sin x = -0.2794

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Question 400808: Help please! Find all the solutions for x to the nearest 0.01 radian in the interval [0,2π] for the equation: sin x = -0.2794
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
You need a calculator (or calculator computer program) for this.

First we find the reference angle. Making sure your calculator is set to radian mode, find sin-1(0,2794). (Note: Do not put the minus sign in. Just use 0.2794!) You should get something close to 0.2831691661234182. (If you got something around 18 then your calculator was in degree mode. Just multiply your answer by pi%2F180 and you should get a number close to mine. 0.2831691661234182 radians is the reference angle.

Next we figure out where angles will have a sin that is negative. We should know that sin's are negative in the same places where y cooridinates are negative, in the 3rd and 4th quadrants.

Now that we have the reference angle and the quadrants, we can find our solutions. In the 3rd quadrant an angle is pi plus the reference angle:
pi+%2B+0.2831691661234182 radians
or
3.1415926535897931 + 0.2831691661234182 radians
or
3.4247618197132113 radians
To the nearest 0.01 radian this would be 3.24 radians.

In the 4th quadrant an angle is 2pi minus the reference angle:
2pi+%2B+0.2831691661234182 radians
or
6.2831853071795862 - 0.2831691661234182 radians
or
6.0000161410561680 radians
To the nearest 0.01 radian this would be 6.00 or just 6 radians

Between 0 and 2pi these are the only two angles with a negative sin and a reference angle of 0.2831691661234182 radians.