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.
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.
The sine function is used in the cross product because the magnitude of the cross product of two vectors is determined by the area of the parallelogram formed by those vectors. This area is calculated as the product of the magnitudes of the vectors and the sine of the angle between them. Specifically, the formula for the cross product (\mathbf{A} \times \mathbf{B}) includes (|\mathbf{A}||\mathbf{B}|\sin(\theta)), where (\theta) is the angle between the vectors, capturing the component of one vector that is perpendicular to the other. Thus, the sine function accounts for the directional aspect of the vectors in determining the resultant vector's magnitude and orientation.
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).
You can use your trigonometric functions (sine, cosine, and tangent).
The inverse (negatives) of sine, cosine, and tangent are used to calculate the angle theta (or whatever you choose to name it). Initially it is taught that opposite over hypotenuse is equal to the sine of theta sin(theta) = opposite/hypotenuse So it can be said that theta = sin-1 (opp/hyp) This works the same way with cosine and tangent In short the inverse is simply what you use when you move the sin, cos, or tan to the other side of the equation generally to find the angle
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.
The sine function is used in the cross product because the magnitude of the cross product of two vectors is determined by the area of the parallelogram formed by those vectors. This area is calculated as the product of the magnitudes of the vectors and the sine of the angle between them. Specifically, the formula for the cross product (\mathbf{A} \times \mathbf{B}) includes (|\mathbf{A}||\mathbf{B}|\sin(\theta)), where (\theta) is the angle between the vectors, capturing the component of one vector that is perpendicular to the other. Thus, the sine function accounts for the directional aspect of the vectors in determining the resultant vector's magnitude and orientation.
The cosine function is used to determine the x component of the vector. The sine function is used to determine the y component. Consider a vector drawn on an x-y plane with its initial point at (0,0). If L is the magnitude of the vector and theta is the angle from the positive x axis to the vector, then the x component of the vector is L * cos(theta) and the y component is L * sin(theta).
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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.
You can use the Pythagorean identity to solve this:(sin theta) squared + (cos theta) squared = 1.
cosine = adjacent/hypotenuse. It can be used as other trig functions can.
Because in dot product we take projection fashion and that is why we used cos and similar in cross product we used sin
To use the right hand rule for the cross product in vector mathematics, align your right hand fingers in the direction of the first vector, then curl them towards the second vector. Your thumb will point in the direction of the resulting cross product vector.
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).