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For the above isosceles triangle with unit sides and angle , the area 1 / 2 × base × height is calculated in two orientations. When upright, the area is sin θ cos θ {\displaystyle \sin \theta \cos \theta } .
Let PQ be a line perpendicular to line OQ defined by angle , drawn from point Q on this line to point P. OQP is a right angle. Let QA be a perpendicular from point A on the x -axis to Q and PB be a perpendicular from point B on the x -axis to P. ∴ {\displaystyle \therefore } OAQ and OBP are right angles.
In mathematics, the values of the trigonometric functions can be expressed approximately, as in (/), or exactly, as in (/) = /.While trigonometric tables contain many approximate values, the exact values for certain angles can be expressed by a combination of arithmetic operations and square roots.
is the number of collisions made (in ideal conditions, perfectly elastic with no friction) by an object of mass m initially at rest between a fixed wall and another object of mass b 2N m, when struck by the other object. [1] (This gives the digits of π in base b up to N digits past the radix point.)
x is the argument of the complex number (angle between line to point and x-axis in polar form). The notation is less commonly used in mathematics than Euler's formula, e ix, which offers an even shorter notation for cos x + i sin x, but cis(x) is widely used as a name for this function in software libraries.
A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle in which one full rotation is 360 degrees. [ 4 ] It is not an SI unit —the SI unit of angular measure is the radian —but it is mentioned in the SI brochure as an accepted unit . [ 5 ]
The sine and tangent small-angle approximations are used in relation to the double-slit experiment or a diffraction grating to develop simplified equations like the following, where y is the distance of a fringe from the center of maximum light intensity, m is the order of the fringe, D is the distance between the slits and projection screen ...
The total curvature of a closed curve is always an integer multiple of 2 π, where N is called the index of the curve or turning number – it is the winding number of the unit tangent vector about the origin, or equivalently the degree of the map to the unit circle assigning to each point of the curve, the unit velocity vector at that point.