The measure of Ø of an angle in standard position is given.
a. Write each degree measure in radians and each radian measure in degrees rounded to the nearest degree.
g. Find the exact values of cos Ø and sin Ø for each angle measure
5π/6 radians
a.
5π/6 radians ≈ 150°
π/3 radians ≈ 60°
g.
cos(5π/6) = -1/2
sin(5π/6) = √3/2
show your work
a. To convert radians to degrees, we multiply by 180/π. To convert degrees to radians, we multiply by π/180. Using these formulas, we get:
5π/6 radians * 180/π ≈ 150°
π/3 radians * 180/π ≈ 60°
To round to the nearest degree, we look at the decimal part of the degree measure. If it is less than 0.5, we round down. If it is greater than or equal to 0.5, we round up. In this case, both degree measures are exact integers, so we don't need to round.
g. To find the exact values of cos and sin, we need to reference the unit circle. For an angle of 5π/6 radians, we can see that it terminates in the second quadrant at the point (-1/2, √3/2).
Using the coordinates of the point, we get:
cos(5π/6) = -1/2
sin(5π/6) = √3/2
a. To convert radians to degrees, use the conversion factor of π radians = 180 degrees.
Converting 5π/6 radians to degrees:
5π/6 radians * (180 degrees / π radians) = (5 * 180) / 6 degrees = 150 degrees
To convert degrees to radians, use the conversion factor of π radians = 180 degrees.
Converting 150 degrees to radians:
150 degrees * (π radians / 180 degrees) = (150 * π) / 180 radians = (5π/6) radians
g. To find the exact values of cos Ø and sin Ø, you'll need to use the unit circle or trigonometric identities.
For 5π/6 radians:
Using the unit circle, we can determine that cos (5π/6) = -√3/2
Similarly, sin (5π/6) = 1/2
Therefore, the exact values of cos Ø and sin Ø for the angle measuring 5π/6 radians are -√3/2 and 1/2, respectively.