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The easiest way of estimating trig values is to visualize the unit circle. (See first link.) In a unit circle (just means the radius is equal to one), draw a horizontal (x) and vertical (y) line through the center. Draw two vertical lines at the intersection of the horizontal line with each side of the circle. Draw a ray from the center of the circle out. The angle you are interested in is the one from the horizontal line straight out to the right, counter-clockwise to the ray you are drawing. A vertical line dropped from the ray where it meets the circle to the horizontal line is the Sine of the angle. This varies from 0 at 0°, to 1 at 90°, back to 0 at 180°, down to -1 at 270°, and finally back to 0 at 360°, which is zero as well. With this information, you could plot a sine curve - and always get it right. With this diagram, it's easy to see that Cosine is negative from 90° around to 270°, and positive elsewhere (except at 90 and 270 where it's zero). The Tangent lines are not quite as easy, but I'm not exactly sure how to send you my diagram. I'll try to explain; The vertical lines on each side of the circle describe the Tangent. Between 0 to 90°, the tangent is positive, which I show with a black line. At 0° it's zero, and at 90° it's undefined - because the ray never meets it. Less than zero, between 0° clockwise and 270°, it takes on negative values, which I show with a red line. So the tangent line on the right is black above and red below. The tangent line on the left is black below and red above, exactly the opposite. To remember which trig value is which, remember Sincostan, the great Indian chief. He led a visitor around; when he showed off all his horses, the visitor exclaimed Oh! When he showed off his warriors, the visitor said Ah! And when the great chief showed off his wives, the visitor said Oh, Ah! - and fainted. Yes, it's a silly story and I didn't tell it well. You can find different versions. Sin=O/H, opposite over hypotenuse. Cos=A/H, adjacent over hypotenuse. Tan=O/A, opposite over adjacent; also sin/cos. Sec is 1/cos, csc=1/sin, and cot=1/tan - and they aren't used as often, either. One last huge memorization task in Trig class is principal values. The only way to remember these is to play with the triangles they are derived from. If you cut a square in half at the opposite corners, you end up with two identical triangles with 45-45-90° corners. The long side, across from the 90° angle, is the hypotenuse and it's 1.414 times the other sides; this is the square root of two. So the Sine of 45° is opposite over hypotenuse, 1/√2. The Cosine of 45° is adjacent over hypotenuse, 1/√2 - so both are equal. The Tangent of 45° is O/A, 1/1=1. The 30-60-90 triangle I'll leave to a better teacher, check the second link. Finally, the third link is a Word document with my actual diagram (a quickie, can't find my copy either). Sorry if it doesn't work.