How do I know when to use sine, cosine, or tangent when solving a vector?

Physics

1 answer:

g100num [7]3 years ago

3 0

Answer:

It depends on what values you know and what is your unknown.

Explanation:

When you investigate the components of a vector, you normally use component in two axes which are perpendicular to each other, and decompose the vector in component in such axes.

The fact that the components are perpendicular is quite important, because you can use trigonometric functions associated with a right angle triangle (see attached figure).

Once you have clear which of the two acute angles is going to be used to define the trigonometric relationships, you can immediately assign the following names to the vector components and to the vector itself. Please look at the picture.

The component "opposite" to the angle you will be using is referred to as "opp" in the image (this is pictured in blue). The component "adjacent" to the angle of reference is called "adj" in the image and pictured in green,

The actual vector is the "hypotenuse" of the right angle triangle defined by the vector and its components and referred as "hyp" in the picture (pictured in red in the image).

Now, depending on what component you need to find, you use the most convenient trig relationship (the one that has more known values) to find an unknown. These relationships are:

$sin(\theta) = \frac{opp}{hyp} \\cos(\theta) = \frac{adj}{hyp} \\tan(\theta)= \frac{opp}{adj}$

and solve in the selected simple ratio for the unknown.

You might be interested in

An electronic balance shows the mass of a sample of sodium chloride to be 29.732 g. what is the uncertainty of the measurement

OLEGan [10]

The uncertainty of the measurement is 0.001 gm.

The uncertainty in the measurement of a physical quantity is given as how precisely we can measure that, in this case as we can see that the mass of the sodium chloride is precisely given as 29.732 gm, this means the electronic scale is precise to 0.001 gm and round of the values after that which means there is a uncertainty of 0.001 gm.

8 0

3 years ago

A wire is oriented along the x-axis. It is connected to two batteries, and a conventional current of 2.4 A runs through the wire

Deffense [45]

Answer:

$\vec{F}=0.40176 N \hat{k}$

Explanation:

To calculate the force we need to use this equation

$\vec{F}=\int\limits^L_0 {i(\vec{dl}\times\vec{B})}$

where L is the total length of the wire

So in this case the small element of current is

$\vec{dl} = dx \hat{i}$

Because x is the direction of the current flow.

As is said in the problem B is such that

$\vec{B} = B \hat{j} = 0.62\hat{j} [ T]$

so to use the equation above we first calculate the following cross product:

$\vec{dl}\times\vec{B}=dx \hat{i}\times B \hat{j} = Bdx\hat{k}$

so the force:

$F = \int\limits^L_0 {i(\vec{dl}\times\vec{B})}=\int\limits^L_0{iBdx\hat{k}}$

So here we use the fact that B=0 in any point of the x axis that is not $x^{'}=0.27 [m]$ , that means that we only need to do the integration between a very short distant behind the point $x^{'}=0.27 [m]$ and a very short distant after that point, meaning: