Suppose an arc of length $s$ lies on the unit circle $x ^ { 2 } + y ^ { 2 } = 1$, starting at point $( 1,0 )$ and terminating at the point ( $x$, $y$ ). Use a calculator to find the approximate coordinates $( x , y )$. Round coordinates to four decimal places when appropriate.

The unit circle $x ^ { 2 } + y ^ { 2 } = 1$
-s = 5.6
A)(-0.7756, °°°)
B)(-0.6313, 0.7756)
C)(0.7756, -0.6313)
D)(-0.7756, -0.6313)

Question

Suppose an arc of length $s$ lies on the unit circle $x ^ { 2 } + y ^ { 2 } = 1$, starting at point $( 1,0 )$ and terminating at the point ( $x$, $y$ ). Use a calculator to find the approximate coordinates $( x , y )$. Round coordinates to four decimal places when appropriate.

The unit circle $x ^ { 2 } + y ^ { 2 } = 1$
-s = 5.6
A)(-0.7756, °°°) 
B)(-0.6313, 0.7756) 
C)(0.7756, -0.6313) 
D)(-0.7756, -0.6313)

Quizplus · Accepted Answer

The correct answer is C because s = 5.6 is in the fourth quadrant, and the sine of an angle in the fourth quadrant is positive and the cosine is negative.

Suppose an Arc of Length sss Lies on the Unit Circle x2+y2=1x ^ { 2 } + y ^ { 2 } = 1x2+y2=1

Suppose an Arc of Length $s$ Lies on the Unit Circle $x ^ { 2 } + y ^ { 2 } = 1$