Please show me the work so i understand

2. Find the reference angle of -11π/3.

5. If �θ = –18°, find the exact value of θ� in radians.

6.If �θ = 3, find the value of �θ in degrees correct to the nearest tenth of a degree.

13.The radius of a circle is 6 inches. If the central angle is 5π/3, find the length of the intercepted arc. (Round to the nearest hundredth.)

2.

-11π/3 + 4π = π/3

5.
-18° * π rad/180° = π/10 radians

6.
3rad * 180°/πrad = 540/π = 171.9°

13.
s = rθ = 6*5π/3 = 10π = 31.42 in

Sure! Let's go through each question step by step and explain the process.

2. Find the reference angle of -11π/3:

To find the reference angle, we first need to determine the quadrant in which the angle lies. Since the angle is negative, we know it lies in either the third or fourth quadrant.

To find the reference angle, we take the absolute value of the angle and then subtract it from 2π (or 360°) if it's in radians, or subtract it from 180° if it's in degrees.

In this case, we have -11π/3 as our angle. The absolute value of -11π/3 is 11π/3. Since this angle is in radians, we subtract 11π/3 from 2π.

Reference angle = 2π - 11π/3
Reference angle = (6π/3) - (11π/3)
Reference angle = (6-11)π/3
Reference angle = -5π/3

So, the reference angle for -11π/3 is -5π/3.

5. If θ = -18°, find the exact value of θ in radians:

To convert degrees to radians, we use the formula: Radians = Degrees * (π/180).

In this case, we have -18° as our angle. To convert it into radians, we multiply it by (π/180).

θ in radians = -18° * (π/180)
θ in radians = -18π/180
θ in radians = -π/10

So, the exact value of θ in radians is -π/10.

6. If θ = 3, find the value of θ in degrees correct to the nearest tenth of a degree:

To convert radians to degrees, we use the formula: Degrees = Radians * (180/π).

In this case, we have θ = 3 in radians. To convert it into degrees, we multiply it by (180/π).

θ in degrees = 3 * (180/π)
θ in degrees ≈ 171.887° (rounded to the nearest tenth)

So, the value of θ in degrees correct to the nearest tenth of a degree is approximately 171.9°.

13. The radius of a circle is 6 inches. If the central angle is 5π/3, find the length of the intercepted arc (rounded to the nearest hundredth):

The formula to find the length of an intercepted arc in a circle is: Arc length = (central angle/360°) * (2π * radius)

In this case, we have a central angle of 5π/3 and a radius of 6 inches.

Arc length = (5π/3)/(2π) * (2π * 6)
Arc length = (5/3)*(6)
Arc length = 10 inches

So, the length of the intercepted arc is 10 inches (rounded to the nearest hundredth).