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Hello. In a mathematic book that I have, there are about 30 formulas to calculate trigonometric functions. Some of them are:
sin(2*pi - x) = sin(x) cos(2*pi - x) = cos(x) sin(2*pi + x) = sin(x) cos(2*pi + x) = cos(x) sin(pi - x)= sin(x) cos(pi - x)= -cos(x) sin(pi + x) = -sin(x) cos(pi + x) = -cos(x) sin(pi/2 - x)= cos(x) cos(pi/2 - x) = sin(x) sin(pi/2 + x) = cos(x) cos(pi/2 + x)= -sin(x) sin(-x) = -sin(x) cos(-x) = cos(x)
and many other similar formulas for tan() and cot(). The question I have is that these formulas are hard to remember and one may forget these formulas in a long time, I'm looking for an easy way to remember these formulas. Is there an easy way to calculate these values, say, sin(5 * (pi/6)) or cos(5 * (pi/6))? Can I just calculate sin() or cos() of (pi/6), and then specify the sign of the result according to the coordinates of the point? For example, 5 * (pi/6) is in the second quarter of the unit circle and in this quarter, sin() is positive and cos() is negative, so the result of sin(5 * (pi/6)) would be (1/2) and cos(5 * (pi/6)) would be (-sqrt(3)/2). Am I correct? 46.224.147.50 ( talk) 17:56, 14 May 2015 (UTC)
sin(pi + x) = -sin(x) cos(pi + x) = -cos(x) sin(pi/2 - x)= cos(x) sin(-x) = -sin(x) cos(-x) = cos(x)
Mathematics desk | ||
---|---|---|
< May 13 | << Apr | May | Jun >> | May 15 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Hello. In a mathematic book that I have, there are about 30 formulas to calculate trigonometric functions. Some of them are:
sin(2*pi - x) = sin(x) cos(2*pi - x) = cos(x) sin(2*pi + x) = sin(x) cos(2*pi + x) = cos(x) sin(pi - x)= sin(x) cos(pi - x)= -cos(x) sin(pi + x) = -sin(x) cos(pi + x) = -cos(x) sin(pi/2 - x)= cos(x) cos(pi/2 - x) = sin(x) sin(pi/2 + x) = cos(x) cos(pi/2 + x)= -sin(x) sin(-x) = -sin(x) cos(-x) = cos(x)
and many other similar formulas for tan() and cot(). The question I have is that these formulas are hard to remember and one may forget these formulas in a long time, I'm looking for an easy way to remember these formulas. Is there an easy way to calculate these values, say, sin(5 * (pi/6)) or cos(5 * (pi/6))? Can I just calculate sin() or cos() of (pi/6), and then specify the sign of the result according to the coordinates of the point? For example, 5 * (pi/6) is in the second quarter of the unit circle and in this quarter, sin() is positive and cos() is negative, so the result of sin(5 * (pi/6)) would be (1/2) and cos(5 * (pi/6)) would be (-sqrt(3)/2). Am I correct? 46.224.147.50 ( talk) 17:56, 14 May 2015 (UTC)
sin(pi + x) = -sin(x) cos(pi + x) = -cos(x) sin(pi/2 - x)= cos(x) sin(-x) = -sin(x) cos(-x) = cos(x)