Normally you use sine theta with the cross product and cos theta with the vector product, so that the cross product of parallel vectors is zero while the dot product of vectors at right angles is zero.
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That is how the scalar product is defined. Also, the projection of one vector onto another at an angle to it is directly proportional to the cosine of that angle.
A reciprocal trigonometric function is the ratio of the reciprocal of a trigonometric function to either the sine, cosine, or tangent function. The reciprocal of the sine function is the cosecant function, the reciprocal of the cosine function is the secant function, and the reciprocal of the tangent function is the cotangent function. These functions are useful in solving trigonometric equations and graphing trigonometric functions.
cosine = adjacent/hypotenuse. It can be used as other trig functions can.
Work is defined as the dot product of force times distance, or W = F * d = Fd cos (theta) where theta is the angle in between the force and distance vectors (if you are doing two dimensions). In three dimensions, use the standard definition for the dot product (using the component form of the vectors).
In trigonometry, theta is a symbol commonly used to represent an unknown angle in the same way you might use x to label an unknown side or an unknown number in general. Theta looks like this: θ