Use a compass to sketch a quarter of a circle of radius 10 centimeters.Using a protractor, construct an angle of in standard position (see figure).Drop a perpendicular line from the point of intersection of the terminal side of the angle and the arc of the circle.By actual measurement, calculate the coordinates of the point of intersection and use these measurements to approximate the six trigonometric functions of a angle.(Round your answer to two decimal places.)

A)sin10° ≈ 0.98, cos10° ≈ 0.17, tan10° ≈ 5.76, csc10° ≈ 0.18, sec10° ≈ 1.02, cot10° ≈ 5.67
B)sin10° ≈ 5.67, cos10° ≈ 1.02, tan10° ≈ 5.76, csc10° ≈ 0.18, sec10° ≈ 0.98, cot10° ≈ 5.67
C)sin10° ≈ 0.17, cos10° ≈ 0.98, tan10° ≈ 0.18, csc10° ≈ 5.76, sec10° ≈ 1.02, cot10° ≈ 5.67
D)sin10° ≈ 0.18, cos10° ≈ 0.98, tan10° ≈ 0.17, csc10° ≈ 10, sec10° ≈ 0.98, cot10° ≈ 5.76
E)sin10° ≈ 0.17, cos10° ≈ 0.98, tan10° ≈ 0.18, csc10° ≈ 5.76, sec10° ≈ 5.67, cot10° ≈ 1.02

Question

Use a compass to sketch a quarter of a circle of radius 10 centimeters.Using a protractor, construct an angle of  in standard position (see figure).Drop a perpendicular line from the point of intersection of the terminal side of the angle and the arc of the circle.By actual measurement, calculate the coordinates  of the point of intersection and use these measurements to approximate the six trigonometric functions of a  angle.(Round your answer to two decimal places.)
​  ​
A)sin10° ≈ 0.98, cos10° ≈ 0.17, tan10° ≈ 5.76, csc10° ≈ 0.18, sec10° ≈ 1.02, cot10° ≈ 5.67 
B)sin10° ≈ 5.67, cos10° ≈ 1.02, tan10° ≈ 5.76, csc10° ≈ 0.18, sec10° ≈ 0.98, cot10° ≈ 5.67 ​ 
C)sin10° ≈ 0.17, cos10° ≈ 0.98, tan10° ≈ 0.18, csc10° ≈ 5.76, sec10° ≈ 1.02, cot10° ≈ 5.67 ​ 
D)sin10° ≈ 0.18, cos10° ≈ 0.98, tan10° ≈ 0.17, csc10° ≈ 10, sec10° ≈ 0.98, cot10° ≈ 5.76 ​ 
E)sin10° ≈ 0.17, cos10° ≈ 0.98, tan10° ≈ 0.18, csc10° ≈ 5.76, sec10° ≈ 5.67, cot10° ≈ 1.02

Quizplus · Accepted Answer

The point of intersection is approximately (-9.40, 1.67). 
Using this point, we can set up the trigonometric functions:

sin(10°) ≈ opposite/hypotenuse ≈ 1.67/10 ≈ 0.17 
cos(10°) ≈ adjacent/hypotenuse ≈ -9.40/10 ≈ -0.94 (note that the x-coordinate is negative in the third quadrant) 
tan(10°) ≈ opposite/adjacent ≈ 1.67/-9.40 ≈ -0.18 
csc(10°) ≈ hypotenuse/opposite ≈ 10/1.67 ≈ 5.98 
sec(10°) ≈ hypotenuse/adjacent ≈ 10/-9.40 ≈ -1.06 
cot(10°) ≈ adjacent/opposite ≈ -9.40/1.67 ≈ -5.62

Therefore, the correct answer is choice C.

Use a Compass to Sketch a Quarter of a Circle