3. Unit Circle

Given the function $y=3\cdot \sin \left(2x\right)$, what are its amplitude and period?

The unit circle has been divided into twelve equal arcs, corresponding to t-values of

0, 𝜋/6, 𝜋/3, 𝜋/2, 2𝜋/3, 5𝜋/6, 𝜋, 7𝜋/6, 4𝜋/3, 3𝜋/2, 5𝜋/3, 11𝜋/6, and 2𝜋

Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.

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sin 𝜋/6

Find a calculator approximation to four decimal places for each circular function value. See Example 3.

cot 6.0301

Find a calculator approximation to four decimal places for each circular function value. See Example 3. sin 0.6109

On the unit circle, if point A is at $(1,0)$ and point D is at $(0,1)$, what is the measure in radians of the arc from A to D (arc AD)?

Given $x=\sin \frac{\pi }{2}$ and $y=\cos \frac{\pi }{2}$, which of the following is correct for $x$ and $y$ where $0\le \theta \le \pi$?

Use a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. cos(30° + 20°) = cos 30° + cos 20°

Concept Check Work each problem. Find the equation of the line that passes through the origin and makes a 30° angle with the x-axis.

Which of the following situations can be modeled with a periodic function?

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.

Which expression is equivalent to $\sin \frac{7\pi }{6}$?

On the unit circle, what is the radian measure of the arc that subtends a central angle of $90°$?

Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. See Example 6. √3 cot θ = - —— 3

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

[π/2, π] ; sin s = 1/2