+ If we consider the unit circle, start at t = 0, and traverse the circle counterclockwise, we may view the height, h, of the traversing point as a function of the angle, t, in radians. From there, we can plot the resulting (t,h) ordered pairs and connect them to generate the circular function f(t) pictured in the following figure. This function tracks the height of a point traversing the unit circle, so that h=f(t) is the height of the point at angle t.
+
+
graph of a unit circle and moveable point on the circle
@@ -155,8 +160,8 @@
Complete the following table with the exact values of h that correspond to the stated inputs.
-
-
+
+ t0$anglelist[1]
@@ -164,7 +169,7 @@
$anglelist[3]$anglelist[4]
-
+ hvalue of h0value of h$plist[1][2]
@@ -172,7 +177,7 @@
value of h$plist[3][2]value of h$plist[4][2]
-
+ t$anglelist[5]$anglelist[6]
@@ -180,7 +185,7 @@
$anglelist[8]$anglelist[9]
-
+ hvalue of h$plist[5][2]value of h$plist[6][2]
@@ -188,7 +193,7 @@
value of h$plist[8][2]value of h$plist[9][2]
-
+ t$anglelist[10]$anglelist[11]
@@ -196,7 +201,7 @@
$anglelist[13]$anglelist[14]
-
+ hvalue of h$plist[10][2]value of h$plist[11][2]
@@ -204,7 +209,7 @@
value of h$plist[13][2]value of h$plist[14][2]
-
+ t$anglelist[15]$anglelist[16]
@@ -212,7 +217,7 @@
-
+ hvalue of h$plist[15][2]value of h$plist[16][2]
@@ -228,11 +233,11 @@
What is the exact value of f\left(\frac{11\pi}{4}\right)?
- -sqrt(2)/2
+ sqrt(2)/2
What is the exact value of f\left(\frac{14\pi}{3}\right)?
- -sqrt(3)/2
+ sqrt(3)/2