What is the difference between sine and cosine?
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sine: In a right triangle, the ratio of the length of the side opposite an acute angle to the length of the hypotenuse.\ncosine: In a right triangle, the ratio of the length of the side adjacent to an acute angle to the length of the hypotenuse.
299290
First is the spelling.  It's trigonometry.\n\nSecond is the question.  You would need to be more specific.  There are many good online sources for that.  Just google it and search the sites.  There will be some university level sites or some simpler ones too.
463801
The cosine laws apply to triangles which are NOT right angled. I think you have maybe read that wrong:\n\nhttp://www.themathpage.com/aTrig/law-of-sines.htm\n\ngives you a full guide to using the cosine laws to solve problems like these.
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sin(θ) ≈ θ\nSo cos (θ) ≈ 1  because cos (0) = 1\nMore accurately cos (θ) ≈ 1 - θ²/2
319082
RHS cot a - tan b \n= cos a/sina - sinb/cosb \n= cosacosb - sinasinb/sinacosb\n= cos(a+b)/sinacosb\n= LHS (proven)\n\nThe idea is to prove that both sides are the same.
77303
The question is actually asking you if cosine(x) is a continuous function. if a function is continuous, lim(f(x)) as x approach a is f(a).\n\na function is continuos if the following criteria are satisfied:\n1. the function f(x) exists for all x\n2. for all x, lim(f(x)) from the positive side = lim from the negative side for all points.\n\n\nnow since cosine(x) is a function that satisfies both criteria, cos(x) is continuous and therefore lim(cos(x)) as x approaches a is just cos(a).
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Actually, when the answers come out as negative, it's calculating in radians. So the sine of 6 is negative, as it is actually calculating about 324 degrees.\n\n2nd+0 resets your calculator, but i don't recommend it.
797707
See the picture:\n\nhttp://mudandmuck.com/str2/sin&cos.jpg\n\nThe two triangles in the picture are equivalent.  (Same angles, and one side of each we know to be the same (hypotenuse=1), so all the sides have the same absolute length, only their signs are different.)
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This ratio is called the cosine.
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sin(pi/2 + x) = sin (pi/2)cosx + cos(pi/2)sinx\n\n= 1cosx + 0 = cosx\n\ncos(-x)=cos(x)\n\nSo cos(x)cos(x) = cos^2(x)
59453
Using your unit circle, you can see that:\nsin 30 = sin 150 = -sin 210 = -sin 330 and\ncos 10 = cos 350 = -cos 170 = -cos 190\n\nThis illustrates some basic identities which you should memorize, namely that\n\nsin (180 - x) = sin x and sin (-x)= - sin x\nand\ncos (180 - x) = -cos x and cos (-x) = cos x\n\nThese are probably in the front or back cover of your textbook.  :)
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It's spelled "pi" and it's used in trigonometry because it's how you measure a circle in radians. Radians is a better way to measure angles - pi is equivalent to 180 degrees, and 2pi is equivalent to 360 degrees.
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Take a unit circle and a point p on the circle. Embed the circle to be centered at the origin on a Cartesian xy-plane. The cosine of p, cos(p), is the x-coordinate, or abscissa, of p. The sine of p is the y-coordinate. These functions are the projection functions for the unit circle. \nIt is common to give the points p on the 1-dimensional circle the coordinate referring to the arclength between p and the positive x-axis (as measured clockwise). Thus, the point (1, 0) on the unit circle is given the native coordinate (0), or 0 for short. Inversely, the point 0 in the unit circle has Cartesian coordinates (cos(0), sin(0)). Since the circumference of a circle is 2Pi, a point that is a quarter of the way around the circle from the positive x-axis is given the coordinate 2Pi/4 = Pi/2 and so forth. This system of coordinates is called radians and is the native way of measuring angles, as each angle has a unique radian measure. \nThis relationship can be seen by drawing a radius from the origin to mark the angle and assigning it the radian measure of wherever it intersects the unit circle. There are more analytical reasons as well, as you go on to study calculus.\nThe radius drawn above also gives the relationship between these circular projection functions, and the way one first encounters trigonometric functions, as ratios of the sides of right triangles. Now you should be able to visualize the triangles inside the unit circle (or any larger circle, dependent on the triangle's hypotenuse), and see why the trigonometric functions are cyclic in 2Pi, and derive some properties of the trigonometric functions that are not easily apparent from just looking at right triangles.\nThe tangent function is so named because it is the length of a certain tangent to the circle; a tangent drawn from the positive x-axis to where it meets an extended radius of the circle. You may be able to work out the equation tan(p) = sin(p)/cos(p) from the geometry involved. If you're familiar with the secant function, (1/cos(p)), you may want to know that it is a geometric secant as well. See the sources below for pictures.
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= cosx[cosxcosy+sinxsiny]+sinx[sinxcosy-cosxsiny]\n\n= (Cosx)^2cosy+cosxsinxsiny+(sinx)^2cosy-cosxsinxsiny\n\n= (Cosx)^2cosy + (Sinx)^2cosy\n\n= Cosy [ (cos)x^2 + (sinx)^2]\n\n= Cos(y)
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integral of sine squared.\nso theres a conversion thing which says \nsin^2 x = (1-cos 2x)/2\nso if you use that then u have to integrate 1/2 - cos 2x/2\nwhich is just 1/2x - sin 2x / 4
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The site below, around one-third of the way down, shows the geometry needed to answer your question.\n\nOnce you have the formula for cos(A+B), namely cosAcosB - sinAsinB, the proof is easy. Just substitute -B for B, and you get\n\ncos(A-B) = cosAcos(-B) - sinAsin(-B)\n\nNow, cos(-B) = cosB and sin(-B) = -sin(B). Thus\n\ncos(A-B) = cosAcosB + sinAsinB
400641
There's a difference.  It refers to (sin x)^2.  Plug in a few numbers and you can easily tell the difference.