Find the polar coordinates of each point with the given rectangular coordinates. Use degrees. (-4,-3)
r = sqrt (4^2+3^2)
which we know is 5 because of 3 4 5 right triangle so we do not need c^2=a^2+b^2
-4 = 5 cos theta
cos theta = -4/5
theta = 143 if you use your calculator but that would be wrong because we are in QUADRANT 3 where sin and cos BOTH negative
cos^-1 4/5 = 36.9
so theta = 180 + 36.9 = 217 degrees
so
r = 5 , theta = 217
To find the polar coordinates of a point given the rectangular coordinates (x, y), you can use the following formulas:
r = √(x^2 + y^2)
θ = arctan(y / x)
In this case, the rectangular coordinates given are (-4, -3).
Step 1: Calculate the value of r:
r = √((-4)^2 + (-3)^2)
= √(16 + 9)
= √25
= 5
Step 2: Calculate the value of θ:
θ = arctan((-3) / (-4))
Since both x and y are negative in this case, the resulting angle will be in the second quadrant, between 90 and 180 degrees.
θ = arctan(3/4)
Using a calculator, you can find that θ is approximately 36.87 degrees.
Therefore, the polar coordinates of the point (-4, -3) are (5, 36.87°).