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Algebra, Trig
Find the radian measure of the central angle of a circle of radius r = 4 inches that intercepts an arc length s = 20 inches.
The formula for an arc length is a = r?, where'd is the arc length, ? is the central angle in radians, and r is the radius. That said, s = 20, r = 4, and ? is unknown.
= 5 radians
The central angle is 5 radians.
In which quadrant will the angle 100 degrees lie in the standard position?
The angle of 100 degrees will lie in Quadrant II.
In which quadrant will the angle -305 degrees lie in the standard position?
The angle of -305 degrees will lie in Quadrant I.
Find the length of the arc on a circle of radius r = 5 yards intercepted by a central angle 0 = 70 degrees.
The formula for an arc length is a = r?, where'd is the arc length, ? is the central angle in radians, and r is the radius. That said, s = unknown, r = 5, and ? = 70 degrees.
degrees converted to radians 1.22 radians s = (5)(1.22) = 6.1 yards.
Answer: The length of the arc is 6.1 yards.
5. Convert the following angle to degrees: n or pie radians converted to degrees ? * 180/? 180 degrees
Answer: radians is equal to 180 degrees.
6. Classify the angle 101 degrees as acute, right, obtuse, or straight.
Answer: The angle of 101 degrees is obtuse.
7. Draw the following angle in standard the position: 7n or 7 pie
Convert to degrees first, which can be gained by the following:
7? * 180/? = 1260 degrees 1260 -- 360 = 900-900 -- 360 = 540
540 -- 360 = 180.
Answer: The angle would be a straight angle with a measure of 180 degrees.
8. Convert -60 degrees to radians. Express the answer as a multiple of pie.
-60 = 300 degrees
Conversion from degrees to ? is the following:
300 * ?/180 = 150?/90 = 5/3?
Answer: -60 degrees is 5/3? radians.
9. Find a co-terminal angle for the following angle: -268 degrees
To find a co-terminal angle, one adds or subtracts 360 degrees into the original angle.
Thus, -268 + 360 = 92 degrees
Answer: 92 degrees.
10. Find the value of (sin 38 degrees) (csc 38 degrees)
sin (38)csc (38) sin (38)*(1/sin (38)) = 1
Answer: 1.
11. Use an identity to find the value of: sin^2-50 degrees + cos^2-50 degrees
The identity is as follows: sin^2 + cos^2 = 1
sin^2(50) + cos^2(50) = 1
Answer: 1.
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