How do I write theta = 45 degrees in rectangular form??
Thanks for your help.
I am not really understanding your question. If you have a vector, as in 23@45, then that vector in cartesian corrdinates is x=23cos45 y=23sin45
The question straight from the book is
"Write theta = 45 degrees in rectangular form."
Thanks
To write the angle theta, which is 45 degrees, in rectangular form, you need to convert it into the corresponding x and y coordinates.
1. Recall that in rectangular coordinates, the x-coordinate represents the horizontal position, and the y-coordinate represents the vertical position.
2. In this case, when theta = 45 degrees, we can visualize it as an angle in the Cartesian coordinate system in the first quadrant.
3. To find the rectangular form, start by recognizing that this angle forms a right isosceles triangle, where both legs are equal. In this triangle, the hypotenuse represents the magnitude, and the legs represent the x and y coordinates.
4. For a right isosceles triangle with a leg length of 1, the x and y coordinates of the endpoint of the hypotenuse will both be 1/sqrt(2). This is because the hypotenuse length is the square root of the sum of the squares of the leg lengths, which is sqrt(1^2 + 1^2) = sqrt(2).
5. Since theta is in the first quadrant, both x and y are positive. Therefore, the rectangular form is x = 1/sqrt(2) and y = 1/sqrt(2).
Therefore, the rectangular form of theta = 45 degrees is (1/sqrt(2), 1/sqrt(2)).
Note: If you need to convert degrees to radians, remember that 180 degrees is equal to pi radians.