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Cos(-x) = -cosx for all values of x.
True or false?

User Hampo
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1 Answer

4 votes

Final answer:

The statement about cosine is false because cosine is an even function, hence cos(-x) equals cos(x). The part about expressing a 2-D vector in terms of its components is true, though they are summed, not multiplied.

Step-by-step explanation:

The statement cos(-x) = -cosx for all values of x is false. This is because the cosine function is an even function, which means that cos(-x) = cos(x) for any angle x. This property is derived from the definition of the cosine function in terms of the unit circle, where cos(-x) and cos(x) correspond to the same horizontal coordinate of a point on the circle.

Moreover, it is true that every 2-D vector can be expressed as the sum (not product) of its x and y components. For a 2-D vector with magnitude A, the x-component can be given as Ax = A cos θ and the y-component as Ay = A sin θ, where θ is the angle the vector makes with the positive x-axis.

User Sowdri
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