The point P=(X, -3/7) lies on the unit circle shown below. What is the value of x in simplest form?
23 answers
Without additional information, it is impossible to determine the value of x in simplest form.
The point P= (x , -3/7) lies on the unit circle shown below. What is the value of x in simplest form?
x is in Quadrant III
x is in Quadrant III
Since the point P lies on the unit circle, we know that its distance from the origin is 1. Using the Pythagorean theorem, we can write:
x^2 + (-3/7)^2 = 1^2
Simplifying this equation, we get:
x^2 + 9/49 = 1
Subtracting 9/49 from both sides, we get:
x^2 = 40/49
Taking the square root of both sides (and remembering that x is negative in Quadrant III), we get:
x = -sqrt(40/49) = -2/7 * sqrt(10)
Therefore, the value of x in simplest form is -2/7 * sqrt(10).
x^2 + (-3/7)^2 = 1^2
Simplifying this equation, we get:
x^2 + 9/49 = 1
Subtracting 9/49 from both sides, we get:
x^2 = 40/49
Taking the square root of both sides (and remembering that x is negative in Quadrant III), we get:
x = -sqrt(40/49) = -2/7 * sqrt(10)
Therefore, the value of x in simplest form is -2/7 * sqrt(10).
Find an angle θ coterminal to 962∘ , where 0∘ ≤ θ <360 ∘
To find an angle θ coterminal to 962∘ within the given range, we can subtract the nearest multiple of 360°.
962° - 2(360°) = 242°
Therefore, an angle θ coterminal to 962° within the given range is 242°.
962° - 2(360°) = 242°
Therefore, an angle θ coterminal to 962° within the given range is 242°.
Find the reference angle for a rotation of 316°.
To find the reference angle for a rotation of 316°, we follow these steps:
1. Identify the quadrant in which the angle lies. A rotation of 316° is equivalent to a rotation of 316° - 360° = -44°. Since -90° < -44° < 0°, the angle is in the fourth quadrant.
2. Find the acute angle between the terminal arm of the angle and the x-axis in the standard position. Since the angle is in the fourth quadrant, the reference angle will be the angle between the terminal arm and the nearest point on the x-axis, which is the horizontal line passing through the initial point. This angle is 44° in magnitude, which is the reference angle for a rotation of 316°.
Therefore, the reference angle for a rotation of 316° is 44°.
1. Identify the quadrant in which the angle lies. A rotation of 316° is equivalent to a rotation of 316° - 360° = -44°. Since -90° < -44° < 0°, the angle is in the fourth quadrant.
2. Find the acute angle between the terminal arm of the angle and the x-axis in the standard position. Since the angle is in the fourth quadrant, the reference angle will be the angle between the terminal arm and the nearest point on the x-axis, which is the horizontal line passing through the initial point. This angle is 44° in magnitude, which is the reference angle for a rotation of 316°.
Therefore, the reference angle for a rotation of 316° is 44°.
Convert the angle -4 radians to degrees, rounding to the nearest 10th.
To convert -4 radians to degrees, we use the conversion factor:
1 radian = 180/π degrees
So, we have:
-4 radians = -4 * (180/π) degrees
Using a calculator to evaluate this expression, we get:
-229.183118052 radians ≈ -229.2 degrees
Rounding to the nearest tenth, we get:
-4 radians ≈ -229.2 degrees
Therefore, the angle -4 radians is approximately equal to -229.2 degrees, rounded to the nearest tenth.
1 radian = 180/π degrees
So, we have:
-4 radians = -4 * (180/π) degrees
Using a calculator to evaluate this expression, we get:
-229.183118052 radians ≈ -229.2 degrees
Rounding to the nearest tenth, we get:
-4 radians ≈ -229.2 degrees
Therefore, the angle -4 radians is approximately equal to -229.2 degrees, rounded to the nearest tenth.
Convert the angle 5 radians to degrees, rounding to the nearest 10th.
To convert 5 radians to degrees, we use the conversion factor:
1 radian = 180/π degrees
So, we have:
5 radians = 5 * (180/π) degrees
Using a calculator to evaluate this expression, we get:
286.478897565 degrees
Rounding to the nearest tenth, we get:
5 radians ≈ 286.5 degrees
Therefore, the angle 5 radians is approximately equal to 286.5 degrees, rounded to the nearest tenth.
1 radian = 180/π degrees
So, we have:
5 radians = 5 * (180/π) degrees
Using a calculator to evaluate this expression, we get:
286.478897565 degrees
Rounding to the nearest tenth, we get:
5 radians ≈ 286.5 degrees
Therefore, the angle 5 radians is approximately equal to 286.5 degrees, rounded to the nearest tenth.
Convert the angle −4.5 radians to degrees, rounding to the nearest 10th.
To convert −4.5 radians to degrees, we use the conversion factor:
1 radian = 180/π degrees
So, we have:
−4.5 radians = −4.5 * (180/π) degrees
Using a calculator to evaluate this expression, we get:
−257.874363601 degrees
Rounding to the nearest tenth, we get:
−4.5 radians ≈ −257.9 degrees
Therefore, the angle −4.5 radians is approximately equal to −257.9 degrees, rounded to the nearest tenth.
1 radian = 180/π degrees
So, we have:
−4.5 radians = −4.5 * (180/π) degrees
Using a calculator to evaluate this expression, we get:
−257.874363601 degrees
Rounding to the nearest tenth, we get:
−4.5 radians ≈ −257.9 degrees
Therefore, the angle −4.5 radians is approximately equal to −257.9 degrees, rounded to the nearest tenth.
Convert the angle 2π radians to degrees.
To convert 2π radians to degrees, we use the conversion factor:
1 radian = 180/π degrees
So, we have:
2π radians = 2π * (180/π) degrees
Simplifying, we get:
2π radians = 360 degrees
Therefore, the angle 2π radians is equal to 360 degrees.
1 radian = 180/π degrees
So, we have:
2π radians = 2π * (180/π) degrees
Simplifying, we get:
2π radians = 360 degrees
Therefore, the angle 2π radians is equal to 360 degrees.
Convert the following angle from degrees to radians. Express your answer in simplest form.
585 degrees
585 degrees
To convert 585 degrees to radians, we use the conversion factor:
1 degree = π/180 radians
So, we have:
585 degrees = 585 * (π/180) radians
Simplifying, we get:
585 degrees = (65π/12) radians
Therefore, the angle 585 degrees is equivalent to (65π/12) radians in simplest form.
1 degree = π/180 radians
So, we have:
585 degrees = 585 * (π/180) radians
Simplifying, we get:
585 degrees = (65π/12) radians
Therefore, the angle 585 degrees is equivalent to (65π/12) radians in simplest form.
that's wrong
I apologize for the mistake in my earlier answer. Here is the correct solution:
To convert 585 degrees to radians, we use the conversion factor:
1 degree = π/180 radians
So, we have:
585 degrees = 585 * (π/180) radians
Simplifying, we get:
585 degrees = (39π/4) radians
Therefore, the angle 585 degrees is equivalent to (39π/4) radians in simplest form.
To convert 585 degrees to radians, we use the conversion factor:
1 degree = π/180 radians
So, we have:
585 degrees = 585 * (π/180) radians
Simplifying, we get:
585 degrees = (39π/4) radians
Therefore, the angle 585 degrees is equivalent to (39π/4) radians in simplest form.
Convert the following angle from degrees to radians. Express your answer in the simplest form.
645 degrees
645 degrees
To convert 645 degrees to radians, we use the conversion factor:
1 degree = π/180 radians
So, we have:
645 degrees = 645 * (π/180) radians
Simplifying, we get:
645 degrees = (43π/4) radians
Therefore, the angle 645 degrees is equivalent to (43π/4) radians in simplest form.
1 degree = π/180 radians
So, we have:
645 degrees = 645 * (π/180) radians
Simplifying, we get:
645 degrees = (43π/4) radians
Therefore, the angle 645 degrees is equivalent to (43π/4) radians in simplest form.
can you Reduce the fraction by dividing out the common
Yes, we can reduce the fraction (43π/4) by dividing out the common factor of π.
Doing so gives:
(43π/4) = 43/4 * π
Therefore, the angle 645 degrees is equivalent to (43/4) π radians in simplest form.
Doing so gives:
(43π/4) = 43/4 * π
Therefore, the angle 645 degrees is equivalent to (43/4) π radians in simplest form.