



 
Hi David, I would use a graphical method to tell me how many solutions there are and their approximate values before attempting to find the solutions. There are two ways I can see to do this. Method 1.
Method 2.
Whichever graph you choose to look at you now know there are two solutions to $\sin 3x = 0.1254 \mbox{ with } 0<x<360^o$ and you know the approximate values of $t = 3x$. Now it's time to use your calculator. When I set my calculator to degrees rather than radians and asked for $\sin^{1}(0.1254)$ I got a response of $7.204^o$. In my first method that's the point $R$ where the angle is measured in a negative direction, clockwise, so measured counterclockwise that's $t = 3x = 360^0  7.204^o$. What's the angle measure of the point $Q?$ In my second method the calculator returned the point $W$ which is $7.204$ units to the left of the origin so $T$ is $7.204$ degrees less than $360.$ What is the $t$ coordinate of $S?$ I am sorry this is so long winded but I don't know which graphical method you prefer. Harley  


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