Find the vector of length 2 making an angle of 45^\circ with the x-axis. round to 6 decimals places or give an exact answer in terms of sine and cosine.

By using trigonometric relations, we will see that the vector is:

V = < 2*cos(45°), 2*sin(45°) >

How to get the components of the vector?

If you think this like a right triangle, we have that the length of the vector is the hypotenuse, the x-component is the adjacent cathetus and the y-component is the opposite cathetus.

Then using the sine and cosine trigonometric relations we will get the components:

x-component = 2*cos(45°) y-component = 2*sin(45°).

Then the vector is just:

V = < 2*cos(45°), 2*sin(45°) >

If you want to learn more about vectors, you can read:

link

For this case we have the following vector:
 v = 2 * (cosine (45) i + sine (45) j)
 Rewriting we have:
 v = 2 * (cosine (45) i + sine (45) j)
 v = 2 * ((0.707107) i + (0.707107) j)
 v = (1.414214) i + (1.414214) j
 
 the vector of length 2 making an angle of 45 with the x-axis is:
 v = (1.414214) i + (1.414214) j

The Answer is C you can find the other two from using tan cos or sin