Convert the Cartesian coordinate (-1,2) to polar coordinates, 0≤θ<2π
I know r is sqrt(5) but how would I find theta between 0 and 2pi?
Thanks in advance!
I see thanks for the help! I forgot to put my calculator on radian mode and got a totally different answer!
To find θ, the angle in polar coordinates, you can use the arctan function. The formula to calculate θ is given as:
θ = arctan(y / x)
In this case, x = -1 and y = 2. Substitute these values into the formula:
θ = arctan(2 / -1)
Now, to find the angle between 0 and 2π, you need to determine the quadrant in which the point (-1, 2) lies. Since x is negative and y is positive, the point lies in the second quadrant.
To get the appropriate angle between 0 and 2π, add π (pi) to the θ obtained from the arctan function:
θ = arctan(2 / -1) + π
Now, you can use a calculator to find the value of arctan(2 / -1) and add π to it to get the final value of θ.
To find the angle θ in polar coordinates, we can use the arctan function (also known as the inverse tangent function). The arctan function allows us to determine the angle between the positive x-axis (the horizontal axis in Cartesian coordinates) and the line connecting the origin to the given point.
In this case, the Cartesian coordinate is (-1, 2). We can calculate the angle θ as follows:
Step 1: Calculate the arctan of the y-coordinate divided by the x-coordinate.
θ = arctan(2 / -1)
Step 2: Since arctan returns a value in the range -π/2 to π/2, we need to adjust the angle based on the signs of the coordinates.
- If both the x and y coordinates are positive (as in this case), no adjustment is needed.
- If the x coordinate is negative and the y coordinate is positive, we add π (180 degrees) to the result.
- If the x coordinate is negative and the y coordinate is negative, we subtract π (180 degrees) from the result.
- If the x coordinate is positive and the y coordinate is negative, we add 2π (360 degrees) to the result.
Since -1 is negative and 2 is positive, we do not need to make any adjustments.
So, the final value of θ is the arctan of 2 divided by -1, which is approximately 2.03444 radians or approximately 116.565 degrees.
Therefore, the polar coordinates for the Cartesian coordinate (-1, 2) are (sqrt(5), 2.03444) in radians or (sqrt(5), 116.565) in degrees.
you know that the point is in quad II and
tanØ = 2/-1
I know that for tanØ= +2, Ø = appr 1.107
so our angle in II is Ø = π-1.107 = 2.0344
so it has to be (5, 2.0344) if you use the form (r,Ø)