A=ax+by and B=cx-dy
If a = 3 , b = 4, c = 5 and d = 2.
Find the direction of -A (in degrees): relative to +x
To find the direction of -A relative to +x, we need to calculate the angle θ that the vector -A makes with the positive x-axis.
The vector -A can be represented as -A = (-ax, -by). Therefore, -A = (-3x, -4y).
The angle θ can be found using the arctangent function:
θ = arctan(-4y / -3x)
Given that a = 3, b = 4, c = 5, and d = 2, the formula becomes:
θ = arctan(-4(2) / -3(5))
Simplifying further:
θ = arctan(-8 / -15)
To find the value of θ, we can calculate the arctan(-8 / -15) using a calculator or math software. This gives us approximately -28.97 degrees.
So, the direction of -A relative to +x is approximately -28.97 degrees.