Find the coordinates of the point at -10 degrees on a circle of radius 2.7 centered at the origin.
Round your answers to three decimal places.
x = r cosθ
y = r sinθ
Now just plug in your numbers
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 the point at -10 degrees on a circle with a radius of 2.7 centered at the origin.
Let's call the angle at -10 degrees theta. The x-coordinate of the point can be found using the cosine function, and the y-coordinate can be found using the sine function.
The cosine function is defined as the adjacent side divided by the hypotenuse, and the sine function is defined as the opposite side divided by the hypotenuse.
Using these definitions, we have:
x-coordinate = radius * cos(theta)
y-coordinate = radius * sin(theta)
Plugging in the given values, we get:
x-coordinate = 2.7 * cos(-10)
y-coordinate = 2.7 * sin(-10)
Calculating the cosine and sine of -10 degrees, we have:
x-coordinate = 2.7 * 0.985
y-coordinate = 2.7 * -0.174
Thus, the coordinates of the point at -10 degrees on a circle with a radius of 2.7 centered at the origin are approximately:
x-coordinate ≈ 2.654
y-coordinate ≈ -0.470
To find the coordinates of a point on a circle, we can use trigonometric functions. In this case, we need to find the coordinates of a point on a circle of radius 2.7 centered at the origin when the angle is -10 degrees.
First, let's convert the angle from degrees to radians. Since the trigonometric functions in most programming languages or calculators require angles to be in radians, we'll need to convert -10 degrees to radians.
To convert from degrees to radians, we use the formula: radians = (π/180) * degrees
So, for -10 degrees, we have: radians = (π/180) * -10 = -0.1745 radians (rounded to four decimal places).
Now, we can find the coordinates of the point using the trigonometric functions cosine and sine.
The x-coordinate of the point is given by: x = radius * cos(angle)
Substituting the values, we get: x = 2.7 * cos(-0.1745)
The y-coordinate of the point is given by: y = radius * sin(angle)
Substituting the values, we get: y = 2.7 * sin(-0.1745)
Now, let's calculate the values of x and y:
x = 2.7 * cos(-0.1745) ≈ 2.688 (rounded to three decimal places)
y = 2.7 * sin(-0.1745) ≈ -0.471 (rounded to three decimal places)
Therefore, the coordinates of the point at -10 degrees on a circle of radius 2.7 centered at the origin are approximately (2.688, -0.471).