Just like most any other set of functions, trigonometric functions are subject to differentiation. Trig functions are cool (at least sin and cos are) because as you differentiate, they cycle through until you get back where you started.
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Calculus is the study of instantaneous and cumulitive growths of functions with respect to two or more variables. Trigonometry is the study of angles, specifically in triangles.
It depends. Between 9th to 12th.
It means there is a fixed relationship between the three sides of a right angled triangle. If you know the length of two of the sides then the third can be calculated. It has other implications in geometry and trigonometry also.
In geometry, angles are studied mostly in relation to each other. In Trigonometry, angles are studied in relation to side lengths and triangles.
Various trigonometric functions, such as sine or cosine, show the relationship between the lengths of sides of a triangle and the angles between those sides. So trigonometry is used to calculate angles, lengths and distances using right triangles. Right triangles are those that have one angle of exactly 90 degrees. Example: You want to find the height of a tree. Measure off a fixed distance from the tree and measure the angle between the ground and the line-of-sight to the top of the tree. The height of the tree = the distance to the tree times the tangent of the angle between the tree and the ground, ie tan(x).