3. Unit Circle

Given the parametric equation $r\left(t\right)=\left(\cos \right(t),\sin (t),t)$, where does the helix lie?

Figure 10.1 should remind you of trigonometric functions you've seen before. Which of the following functions is most directly represented by the coordinates of a point on the unit circle at an angle $\theta$ from the positive x-axis?

Given the polar equation $r^2=\sin \left(2\theta \right)$, which of the following best describes the shape of its graph on the unit circle?

On the unit circle, which trigonometric functions are undefined when $x=0$?

Find the exact values of s in the given interval that satisfy the given condition.

[0 , 2π) ; cos² s = 1/2

In Exercises 28–29, find a cofunction with the same value as the given expression. sin 70°

Which of the following represents the polar equation $r=(\tan 2\pi )(\csc \pi )$ as a rectangular equation?

Find each exact function value. See Example 2.

sin (-4π/3)

Each figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the six circular function values of θ.

Find the exact value of s in the given interval that has the given circular function value.

[3π/2, 2π] ; tan s = -1

(Modeling) Grade Resistance Solve each problem. See Example 3. A 3000-lb car traveling uphill has a grade resistance of 150 lb. Find the angle of the grade to the nearest tenth of a degree.

Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.

sin s = 0.9918