3.4.1: Exercises 3.4

Exercise \(\PageIndex{1}\)

Explain why the domain of tangent is restricted.

Answer

Tangent is undefined whenever cosine is 0.

Exercise \(\PageIndex{2}\)

Explain why the domain of cosecant is restricted.

Answer

Cosecant is undefined whenever sine is 0.

Exercise \(\PageIndex{3}\)

Explain what is meant by the range of a function.

Answer

The range describes the possible output values of the function.

Exercise \(\PageIndex{4}\)

What do the coordinates on the unit circle tell you?

Answer

The x coordinate tells you the value of cosine for that angle and the y coordinate tells you the value of sine for that angle.

Exercise \(\PageIndex{5}\)

Sketch the unit circle from memory. Use Figure 3.4.2 to check your work and add in any values you could not remember.

Answer

Exercise \(\PageIndex{6}\)

\(\displaystyle \tan{\bigg( \frac{\pi}{4}\bigg)}\)

Answer

\(\displaystyle 1\)

Exercise \(\PageIndex{7}\)

\(\displaystyle \cos{\bigg( \frac{-\pi}{4}\bigg)}\)

Answer

\(\displaystyle \frac{\sqrt{2}}{2}\)

Exercise \(\PageIndex{8}\)

\(\displaystyle \sin{\bigg( \frac{3\pi}{4}\bigg)}\)

Answer

\(\displaystyle \frac{\sqrt{2}}{2}\)

Exercise \(\PageIndex{9}\)

\(\displaystyle \csc{\bigg( \frac{-3\pi}{4}\bigg)}\)

Answer

\(\displaystyle -\sqrt{2}\)

Exercise \(\PageIndex{10}\)

\(\displaystyle \sin{\bigg( \frac{3\pi}{2}\bigg)}\)

Answer

\(\displaystyle -1\)

Exercise \(\PageIndex{11}\)

\(f(x) = -2 \sin{(4x)} + 3\)

Answer

\([1,5]\)

Exercise \(\PageIndex{12}\)

\(g(x) = 6\cos{(2x)} -8\)

Answer

\([-14,-2]\)

Exercise \(\PageIndex{13}\)

\(h(x) = -\sin{(x)} -1\)

Answer

\([-2,0]\)

Exercise \(\PageIndex{14}\)

\(f(\theta) =4\sin{(\theta-\pi)}\)

Answer

\([-4,4]\)

Exercise \(\PageIndex{15}\)

Find the ordered pair for the point on the unit circle associated with \(\theta=\frac{5\pi}{4}\)

Answer

\((-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2})\)

Exercise \(\PageIndex{16}\)

Sketch the a unit circle and the angle represented by \(\theta = \frac{7\pi}{6}\). Find the ordered pair where this line intersects the unit circle and label this point on your sketch.

Answer

Exercise \(\PageIndex{17}\)

Sketch the a unit circle and the angle represented by \(\theta = -\frac{2\pi}{3}\). Find the ordered pair where this line intersects the unit circle and label this point on your sketch.

Answer

Exercise \(\PageIndex{18}\)

Find the equation of the line that intersects the unit circle at \(\theta = \pi\) and at \(\theta=\frac{\pi}{3}\). Answer in slope intercept form.

Answer

\(y=\frac{\sqrt{3}}{3} x+\frac{\sqrt{3}}{3}\)