A vector has x component -7.9 and y component 10.5 What is the direction of the vector to the nearest tenth of a degree?
I tried doing tantheta=10.5/-7.9, however I keep getting a negative angle less than one degree which I hope is not right. Help!
you are correct to say that
tanØ = 10.5/-7.9
Try to visualize where that angle is.
Isn't it in the second quadrant?
The tangent is negative in quadrant II and in quadrant IV.
So on your calculator, find the "angle in standard position" by taking
2nd
tan
(10.5/7.9)
=
to get 53.04°
so in quadrant II Ø = 180° - 53.04° = 126.96°
You calculator has been programmed to give you the closest angle to the origin, which would be -53.04, or a clockwise rotation of 53.04, putting you in the fourth quadrant.
Since for any inverse trig function there are 2 possible solutions in one period, you will have to decide what to do with that answer.
Forgot to mention...
if your angle given by your calculator is less than one degree for the above calcuation, I bet your calculator is set to Radians
Look for a button something like DRG, and press it until DEG appears in your display window
To find the direction of a vector given its components, you can calculate the angle using the inverse tangent function. However, in this case, it seems that you encountered a negative angle less than one degree.
The negative angle arises because the inverse tangent function only provides the angle in the range of -90 degrees to +90 degrees. To adjust for this, you need to consider the signs of the vector components to find the correct quadrant in which the angle lies.
Here's how you can do it step by step:
1. Calculate the value of tan⁻¹(y / x) using your calculator, where y is the y-component (10.5) and x is the x-component (-7.9).
tan⁻¹(10.5 / -7.9) ≈ -53.0 degrees
2. Determine the correct quadrant:
- Since the x-component is negative (-7.9), the angle lies in either the third or the fourth quadrant.
- To determine the correct quadrant, check the sign of the y-component.
- If the y-component is positive, the angle lies in the second quadrant. If it is negative, the angle lies in the fourth quadrant.
In this case, since the y-component is positive (10.5), the angle lies in the second quadrant.
3. Adjust the angle: To find the absolute value of the angle in the second quadrant, add 180 degrees to the negative angle.
-53.0 + 180 ≈ 127.0 degrees
Therefore, the direction of the vector to the nearest tenth of a degree is approximately 127.0 degrees in the second quadrant.