plot the point given in polar coordinates and find the corresponding rectangular coordinates for the point.

(-1 , -3pi/4)

I do not understand.

Thank You!

Are you more comfortable thinking in degrees?

-3π/4 radians = -135° ( clockwise)
-135 is coterminal with +225°
so we could write our point as
(-1,225°)
which is the same as (+1 , +45°)

so x = cos45/1 = √2/2
y = sin45/1 = √2/2

the point is (√2/2,√2/2)

To plot the point in polar coordinates (-1 , -3π/4), we first need to understand how to represent polar coordinates.

In polar coordinates, a point is represented by its distance from the origin (denoted by "r") and the angle it makes with the positive x-axis (denoted by "θ").

In this case, the given polar coordinates are (-1 , -3π/4). The value of "r" is -1, which indicates that the point is 1 unit away from the origin in the opposite direction. The value of "θ" is -3π/4, which indicates that the angle is measured counter-clockwise from the positive x-axis by 3π/4 radians.

To find the corresponding rectangular coordinates, we can use the following formulas:
x = r * cos(θ)
y = r * sin(θ)

Substituting the given values, we have:
x = -1 * cos(-3π/4)
y = -1 * sin(-3π/4)

Using trigonometric identities, cos(-3π/4) = -√2/2 and sin(-3π/4) = -√2/2, so:
x = -1 * (-√2/2) = √2/2
y = -1 * (-√2/2) = √2/2

Therefore, the rectangular coordinates for the point represented by the polar coordinates (-1 , -3π/4) are (x, y) = (√2/2, √2/2).

To plot the point (-1, -3π/4) given in polar coordinates and find its corresponding rectangular coordinates, you can use the following steps:

1. Understanding polar coordinates: In polar coordinates, instead of using the x and y coordinates as in rectangular coordinates, we use the distance from the origin (r) and the angle from the positive x-axis (θ) to locate a point.

2. Plotting the point: To plot the point (-1, -3π/4), you need to visualize a polar coordinate system. Start by locating the origin (0,0) on the graph. The distance from the origin to the point is given as -1, which means the point is 1 unit away from the origin, towards the direction exactly opposite to the positive x-axis.

3. Finding the angle: In this case, the angle is given as -3π/4. Since the angle is negative, it means we need to rotate clockwise instead of counterclockwise. To find the reference angle, you can find the equivalent positive angle by adding 2π (360 degrees) to the given angle: -3π/4 + 2π = 5π/4.

4. Converting to rectangular coordinates: To convert the polar coordinates to rectangular coordinates, you can use the following formulas:
- x = r * cos(θ)
- y = r * sin(θ)

Substituting the values, we get:
x = -1 * cos(5π/4)
y = -1 * sin(5π/4)

5. Evaluating the trigonometric functions: Use a calculator to evaluate cos(5π/4) and sin(5π/4):
cos(5π/4) ≈ -0.707
sin(5π/4) ≈ -0.707

6. Finding the rectangular coordinates: Substitute the evaluated values into the respective formulas:
x = -1 * (-0.707) ≈ 0.707
y = -1 * (-0.707) ≈ 0.707

Therefore, the corresponding rectangular coordinates for the point (-1, -3π/4) are approximately (0.707, 0.707).