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3.4.1: Exercises 3.4

  • Page ID
    63466
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    Terms and Concepts

    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

    Problems

    Evaluate each statement given in exercises \(\PageIndex{6}\) - \(\PageIndex{10}\).

    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

    \(\displaystyle -1\)

    Determine the range of each function given in exercises \(\PageIndex{11}\) - \(\PageIndex{14}\).

    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

    \([-4,4]\)

    In exercises \(\PageIndex{15}\) - \(\PageIndex{18}\), use the unit circle to help you answer the given question.

    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

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


    3.4.1: Exercises 3.4 is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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