Question

The point P=(X, -3/7) lies on the unit circle shown below. What is the value of x in simplest form?

Answer 1

[AI-generated answer — Bot]

Without additional information, it is impossible to determine the value of x in simplest form.

Answer 2

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

Answer 3

[AI-generated answer — Bot]

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).

Answer 4

Find an angle θ coterminal to 962∘ , where 0∘ ≤ θ <360 ∘

Answer 5

[AI-generated answer — Bot]

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°.

Answer 6

Find the reference angle for a rotation of 316°.

Answer 7

[AI-generated answer — Bot]

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°.

Answer 8

Convert the angle -4 radians to degrees, rounding to the nearest 10th.

Answer 9

[AI-generated answer — Bot]

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.

Answer 10

Convert the angle 5 radians to degrees, rounding to the nearest 10th.

Answer 11

[AI-generated answer — Bot]

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.

Answer 12

Convert the angle −4.5 radians to degrees, rounding to the nearest 10th.

Answer 13

[AI-generated answer — Bot]

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.

Answer 14

Convert the angle 2π radians to degrees.

Answer 15

[AI-generated answer — Bot]

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.

Answer 16

Convert the following angle from degrees to radians. Express your answer in simplest form.

585 degrees

Answer 17

[AI-generated answer — Bot]

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.

Answer 18

that's wrong

Answer 19

[AI-generated answer — Bot]

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.

Answer 20

Convert the following angle from degrees to radians. Express your answer in the simplest form.

645 degrees

Answer 21

[AI-generated answer — Bot]

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.

Answer 22

can you Reduce the fraction by dividing out the common

Answer 23

[AI-generated answer — Bot]

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.