Because in dot product we take projection fashion and that is why we used cos and similar in cross product we used sin
The sine of 22.5 degrees is 0.383
No angle has a sine function greater than 1.
In a right triangle, the sine of an (non right angle) angle would the ratio of the opposite side (opposite to the angle selected) and the hypotenuse
The longest side of the right angles triangle is called the hypotenuse. Divide the length of the side opposite the chosen angle by the length of the hypotenuse. This is the Sine of the angle.
Sine = Opposite divided by Hypotenuse Opposite is the side of the triangle opposite the angle (in this case the 90o angle). Hypotenuse is the side opposite the right angle in a right angle triangle. Therefore, Sine 90 = 1 because the opposite side and the hypotenuse are the same side, they are both opposite the right 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.
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.
Scalar product (or dot product) is the product of the magnitudes of two vectors and the cosine of the angle between them. It results in a scalar quantity. Vector product (or cross product) is the product of the magnitudes of two vectors and the sine of the angle between them, which results in a vector perpendicular to the plane containing the two original vectors.
no .....the scalar product of two vectors never be negative Yes it can If A is a vector, and B = -A, then A.B = -A2 which is negative. Always negative when the angle is between the vectors is obtuse.
The angle of incidence is the angle between the incident ray and the normal to the surface, while the angle of refraction is the angle between the refracted ray and the normal to the surface. These angles are related by Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media the light is traveling through.
the sine of a 30 degree angle is 0.5
the sine of an angle can't be greater than 1.0
No. The sine of an angle is not directly proportional to the angle. It is a function of the angle, but it is periodic, repeating every 360 degrees of the angle.
kvar can be calculated as follows the a product KVA andt the sine of the angle between the KVA and KW.
kvar can be calculated as follows the a product KVA andt the sine of the angle between the KVA and KW.
It is 1.
An angle can have a sine ratio, not a triangle.