Hey there.I need to be able to preform a sine function without a calculator, preferably in degrees.I won't be working with angles higher than 360.My initial problem was sin(135)*45.254834, which is 32 in degrees.Through radians, it's 3.99911022, which is not the answer I'm looking for. I can't find a clean conversion from one answer to the other.
Not sure what your question is. Normally, in these cases where you are expected to evaluate trig functions without the use of a calculator, the angles will be 30, 45, 60 (and their multiples) and the quadrantal angles (0, 90, 180, and 270). In the problem you gave, a sin(135) is included. Sine is positive in quadrant II, the reference angle is 45 degrees, so I would expect you to be able to come up with sin(135) = sqrt(2)/2. More difficult problems come later when you'll use half angle identities and other trig identities.
My initial problem was sin(135)*45.254834, which is 32 in degrees. No, it's not. The 135 part is degrees. Sin of that is sqrt(0.5) or ~0.7071. That is no longer in degrees or radians. Multiply by the 45.2548 bit and you get 32. Again, not in degrees or radians. By looking at the unit circle, you can see that on 45 degree boundaries (such as 135 degrees), the opposite and adjacent sides of the right triangle are equal. If the hypotenuse is 1, then by Pythagoras, a^2 + a^2 = 1 2 * a^2 = 1 a^2 = 1/2 a = sqrt(2) a ~ .7071 Now that you know the length of the opposite side, you can read the sine directly. sin(135) = opp/hyp sin(135) = .7071 You can't do that with arbitrary angles. You'd need a table of trigonometric functions. But for certain angles it is possible to get exact answers without a table.
