Use a compass to sketch a quarter of a circle of radius 10 centimeters.Using a protractor, construct an angle of $a = 10 ^ { \circ }$ 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 $( x , y )$ of the point of intersection and use these measurements to approximate the six trigonometric functions of a $\text { "a" }$ 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 $a = 10 ^ { \circ }$ 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 $( x , y )$ of the point of intersection and use these measurements to approximate the six trigonometric functions of a $\text { "a" }$ 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

From the diagram, we can see that the x-coordinate of the point of intersection is approximately 1 and the y-coordinate is approximately 0.17. 
Therefore, the six trigonometric functions are:

sin(10°) ≈ 0.17
cos(10°) ≈ 0.98
tan(10°) ≈ 0.18
csc(10°) ≈ 5.76
sec(10°) ≈ 1.02
cot(10°) ≈ 5.67

These values match those given in choice C.

Use a Compass to Sketch a Quarter of a Circle a=10∘a = 10 ^ { \circ }a=10∘

Use a Compass to Sketch a Quarter of a Circle $a = 10 ^ { \circ }$