Can you please help me with this question on my study guide for my trig final? Thanks! I'd also appreciate if you can check out my other postings and check my work for some other study guide questions. I want to make sure I'm ready for my final. :)
3. The rectangular coordinates of a point are given. Find the polar coordinates of each point.
a. (4,0)
b. (0,3)
Polar coordinates are usually R (radius) and angle from the x axis (theta). Theta is usually measured in radians.
Use these formulas to convert:
theta = arcttan y/x
R = sqrt(x^2 + y^2)
(a) (4,0) in (x,y) coordinates becomes
(4,0) in polar (R,theta) coordinates
(b) (0,3) in (x,y) coordinates is
(pi/2, 3) in polar coordinates.
Aaah, so those are the formulas! I'll remember those. That helps so much! You're awesome! Thank you for not just giving me the answers. The point of a study guide is to study and know how to get to an answer. Usually people just give the answer without showing the process. I really appreciate it. :)
I tried converting (0,3) myself, but I can't seem to get your answer. What am I doing wrong?
b. (R, theta)
R = sqrt(x^2 + y^2)
R = sqrt(0^2 + 3^2)
R = 3
theta = arctan y/x
theta = arctan 3/0
theta = 1.249
= (3, 1.249)
Of course! I'd be happy to help you with your trigonometry questions. Let's start by finding the polar coordinates for each given point.
a. (4, 0):
To find the polar coordinates, we need to convert the rectangular coordinates (x, y) to polar coordinates (r, θ).
In this case, since the given point is (4, 0), the x-coordinate is 4 and the y-coordinate is 0.
To find the polar coordinate r, we can use the formula r = √(x^2 + y^2). Substituting the values, we get r = √(4^2 + 0^2) = √16 = 4.
Next, to find the polar coordinate θ, we can use the formula θ = arctan(y/x). Substituting the values, we get θ = arctan(0/4) = 0.
Therefore, the polar coordinates for the point (4, 0) are (r, θ) = (4, 0).
b. (0, 3):
Using the same steps as above, for the given point (0, 3), the x-coordinate is 0 and the y-coordinate is 3.
The polar coordinate r can be found as r = √(x^2 + y^2) = √(0^2 + 3^2) = √9 = 3.
To find the polar coordinate θ, we use the formula θ = arctan(y/x) = arctan(3/0). However, this expression is undefined because division by 0 is not allowed.
In this case, since x is 0, the point lies on the y-axis, which means its angle θ is either 90 degrees or -90 degrees (π/2 or -π/2 radians). Therefore, the polar coordinates for the point (0, 3) can be written as (r, θ) = (3, π/2) or (3, -π/2).
I hope this helps you find the polar coordinates for the given points. Let me know if there's anything else I can assist you with, or if you'd like me to check your work for other study guide questions.