Vector A has magnitude 23 units and direction, counterclockwise from east, of 5.8 degrees. What is the value of its x component to 1 decimal place? Its y component?
This problem seems easy enough but I keep getting the wrong answer using the law of sines. Is there another way to solve this or do I just need to be more careful?
What direction is x, East? and y, North?
the East component is 23cos5.8
the North cmponent is 23sin5.8
I have no idea why you are using the law of sines.
Haha thank you so much I feel so stupid haha
To find the components of a vector, you can use trigonometry. Given the magnitude and direction of vector A, you can break it down into the x and y components.
To find the x component (A_x), you will use the cosine function. The cosine of an angle in a right triangle is equal to the adjacent side divided by the hypotenuse. In this case, the adjacent side is the x component of the vector and the hypotenuse is the magnitude of the vector. Therefore:
A_x = magnitude * cos(direction)
Plugging in the values, we get:
A_x = 23 * cos(5.8 degrees)
Calculating this expression will give us the x component of the vector.
To find the y component (A_y), you will use the sine function. The sine of an angle in a right triangle is equal to the opposite side divided by the hypotenuse. In this case, the opposite side is the y component of the vector and the hypotenuse is the magnitude of the vector. Therefore:
A_y = magnitude * sin(direction)
Plugging in the values, we get:
A_y = 23 * sin(5.8 degrees)
Calculating this expression will give us the y component of the vector.
It's important to ensure that you are using the correct trigonometric function (sine or cosine) for finding the respective components. Also, make sure your calculator is set to the correct angle mode (degrees or radians) when calculating the trigonometric functions.