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**ragnar** To answer the other questions, what you do with the root-3. You enter it into the tan^-1 function and see what spits out. If you want to avoid using a calculator, you can figure it out because tan^-1 is what does the opposite of tan. Thus, find out what value you can put into tan to get out root-3 and this will be equal to what you get out of tan^-1 when you put in root-3. (But you have to do all of this within the interval (-pi/2, pi/2).)

To solve your other problem, divide both sides by cosx. When you do you'll get (sinx)/(cosx) = root-3. But sine over cosine is tangent. So this is the same thing as tanx = 0. Take tan^-1 of both sides and get x = tan^-1(root-3). You've already calculated tan^-1(root-3).

For the second one, subtract root-3 from both sides and get sinx = -root-3. Take sin^-1 of both sides and get x = sin^-1(-root-3). This one doesn't have a nice, easy answer. Get a calculator and enter sin^-1(-root-3).