Graph the unit circle using parametric equations with your calculator set to radian mode. Use a scale of . Trace the circle to find all values of t between 0 and 2 π satisfying the following statement. Round your answers to the nearest ten-thousandth.
A)t = 0.5236, 2.8338
B)t = 0.5236, 2.618
C)t = 0.647, 2.8338
D)t = 2.618, 0.647
E)t = 0.5236, 0.647

Question

Graph the unit circle using parametric equations with your calculator set to radian mode. Use a scale of  . Trace the circle to find all values of t between 0 and 2 π satisfying the following statement. Round your answers to the nearest ten-thousandth.  ​
A)​​t ​ = 0.5236, 2.8338 
B)​​t ​ = 0.5236, 2.618 
C)​​t ​ = 0.647, 2.8338 
D)​t = 2.618, 0.647 
E)​​t ​ = 0.5236, 0.647

Quizplus · Accepted Answer

Using the parametric equations $x=\cos(t)$ and $y=\sin(t)$ in radian mode, we can graph the unit circle. Since the scale is $11ebf5ef_bb7f_40df_95d1_23e2c05ba6b4_TBX9354_11$, the radius of the circle is 1 unit.

To find the values of $t$ that satisfy the statement, we need to trace the circle and find the points that correspond to the given angles.

Using the calculator, we can find that $\cos(0.5236)\approx0.866$ and $\sin(0.5236)\approx0.5$, which corresponds to a point on the unit circle that is in the first quadrant and makes an angle of approximately $0.5236$ radians with the positive $x$-axis.

Similarly, $\cos(2.618)\approx-0.5$ and $\sin(2.618)\approx0.866$, which corresponds to a point on the unit circle that is in the fourth quadrant and makes an angle of approximately $2.618$ radians with the positive $x$-axis.

Therefore, the only choice that includes these two angles is B: $t=0.5236, 2.618$.

Graph the Unit Circle Using Parametric Equations with Your Calculator