Activity 2.3.4.
Answer the following questions exactly wherever possible. If you estimate a value, do so to at least \(5\) decimal places of accuracy.
(a)
The \(x\) coordinate of the point on the unit circle that lies in the third quadrant and whose \(y\)-coordinate is \(y = -\frac{3}{4}\text{.}\)
(b)
The \(y\)-coordinate of the point on the unit circle generated by a central angle opening counterclockwise with one side on the positive \(x\)-axis that measures \(t = 2\) radians.
(c)
The \(x\)-coordinate of the point on the unit circle generated by a central angle with one side on the positive \(x\)-axis that measures \(t = -3.05\) radians. (With the negative radian measure, we view the angle as opening counterclockwise from its initial side on the positive \(x\)-axis.)
(d)
The value of \(\cos(t)\) where \(t\) is an angle in Quadrant II that satisfies \(\sin(t) = \frac{1}{2}\text{.}\)
(e)
The value of \(\sin(t)\) where \(t\) is an angle in Quadrant III for which \(\cos(t) = -0.7\text{.}\)
(f)
The average rate of change of \(f(t) = \sin(t)\) on the intervals \([0.1,0.2]\) and \([0.8,0.9]\text{.}\)
(g)
The average rate of change of \(g(t) = \cos(t)\) on the intervals \([0.1,0.2]\) and \([0.8,0.9]\text{.}\)
