Hi! Can someone please help me with these? Thanks! :)
Directions: Look for the direction angle for vector v. If necessary, round your answer to the nearest tenth of a degree.
1.) v = 8i - 10j
2.) w = -4i - 3j
#1
tanθ = -10/8 = -1.25
θ = -51.3° or 308.7°
Do #2 the same way. Make sure you end up in the right quadrant.
Of course! I'd be happy to help you with these vector problems.
To find the direction angle for a vector, you can use the arctan function. The arctan function takes the ratio of the vertical component (in this case the y-component) to the horizontal component (in this case the x-component) of the vector.
Let's start with the first problem:
1.) v = 8i - 10j
To find the direction angle, we need to find the ratio of the vertical component (-10j) to the horizontal component (8i). We can write this as:
tan(theta) = -10/8
Now, we can use the arctan function to find the angle theta. The arctan function gives us the angle whose tangent is a particular ratio. In this case, we want to find theta, so we can write:
theta = arctan(-10/8)
Using a calculator, we can evaluate this expression to find the direction angle.
Now, let's move on to the second problem:
2.) w = -4i - 3j
Similarly, we need to find the ratio of the vertical component (-3j) to the horizontal component (-4i). We can write this as:
tan(theta) = -3/-4
Again, we can use the arctan function to find the angle theta:
theta = arctan(-3/-4)
Evaluate this expression using a calculator to find the direction angle.
Remember to round your answers to the nearest tenth of a degree, as specified in the directions.
I hope this explanation helps you solve these problems! Let me know if you have any further questions.