Find the coordinates of the point at -45 degrees on a circle of radius 3.6 centered at the origin.
Round your answers to three decimal places.
To find the coordinates of a point on a circle, we can use the formulas:
x = r * cos(θ)
y = r * sin(θ)
where r is the radius of the circle and θ is the angle formed by the point with the positive x-axis.
In this case, the radius is 3.6 and the angle is -45 degrees.
Converting the angle to radians:
-45 degrees = -45 * π / 180 = -π / 4 radians
Now, we can substitute these values into the formulas:
x = 3.6 * cos(-π / 4)
y = 3.6 * sin(-π / 4)
Using a calculator to evaluate these trigonometric functions, we get:
x ≈ 2.548
y ≈ -2.548
Therefore, the coordinates of the point at -45 degrees on a circle of radius 3.6 centered at the origin are approximately (2.548, -2.548).
To find the coordinates of a point on a circle, we can use the trigonometric functions sine and cosine. In this case, we want to find the coordinates of a point on a circle with radius 3.6 centered at the origin, when the angle is -45 degrees.
Firstly, let's convert the angle from degrees to radians. One full rotation around a circle is equal to 2π radians, so we can convert -45 degrees to radians by multiplying it by π/180:
-45 degrees * (π/180) = -π/4 radians
Next, we can use the trigonometric functions cosine and sine to find the x and y coordinates respectively.
The x-coordinate (horizontal distance from the origin) can be found using the cosine function, which gives us:
x = radius * cos(angle)
x = 3.6 * cos(-π/4)
Evaluating this expression, we get:
x = 3.6 * 0.7071
x ≈ 2.543
Round this result to three decimal places: x ≈ 2.543.
The y-coordinate (vertical distance from the origin) can be found using the sine function, which gives us:
y = radius * sin(angle)
y = 3.6 * sin(-π/4)
Evaluating this expression, we get:
y = 3.6 * (-0.7071)
y ≈ -2.543
Round this result to three decimal places: y ≈ -2.543.
Therefore, the coordinates of the point at -45 degrees on a circle of radius 3.6 centered at the origin are approximately (2.543, -2.543).
x = r cosθ
y = r sinθ
Now just plug in your numbers