



 
Hi Jonathan. That question has no answer. Look at a sine wave: all the values of f(x) = sin(x) vary between 1 and 1, because that's the range of the sine function. Your question says sin(theta) = 3, so that's not possible. But, if you meant to say sin(theta) = 0.3, this is how you would solve it. The sine is the ratio of the opposite side to the hypotenuse. Consider a "unit circle" (that's a circle with radius 1). The radius is the hypotenuse, so in this case, the opposite side is 0.3. That's the "y" value on a normal graph, which means either quadrant III or quadrant IV. There are in fact two angles (two values of theta) in which sin(theta) = 0.3. Now if the hypotenuse of a right triangle is 1 and the opposite side is 0.3 (we can ignore the negative sign for the moment), then Pythagoras can tell us the length of the adjacent (x) side. 0.3^{2} + x^{2} = 1^{2}. When I use my calculator to solve this, I get x = ± 0.95. Now we know: We can calculate any of the trigonometric ratios, just be considering their definitions: So you can find all the values. Just remember that some of these will have two answers (because of the +/ on the adjacent length) and some will only have one value (those that don't use the adjacent side). Hope this helps,  


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