Stewart Precalc 6e Chapter 6: Test

1 Degree to Radian · Level 1

Find the radian measures that correspond to the degree measures \(330°\) and \(-135°\).

2 Radian to Degree · Level 1

Find the degree measures that correspond to the radian measures \(\dfrac{4 \pi}{3}\) and \(-1.3\).

3 Angular and Linear Speed · Level 2

The rotor blades of a helicopter are 16 ft long and are rotating at 120 rpm. (a) Find the angular speed of the rotor. (b) Find the linear speed of a point on the tip of a blade.

4 Exact Values · Level 2

Find the exact value of each of the following. (a) \(\sin 405°\) (b) \(\tan(-150°)\) (c) \(\sec \dfrac{5 \pi}{3}\) (d) \(\csc \dfrac{5 \pi}{2}\)

5 Trig Computation · Level 2

Find \(\tan \theta + \sin \theta\) for the angle \(\theta\) shown.

6 Express Lengths in Terms of Theta · Level 2

Express the lengths \(a\) and \(b\) shown in the figure in terms of \(\theta\).

7 Trig Identity Computation · Level 2

If \(\cos \theta = -\dfrac{1}{3}\) and \(\theta\) is in Quadrant III, find \(\tan \theta \cot \theta + \csc \theta\).

8 Trig Identity Computation · Level 2

If \(\sin \theta = \dfrac{5}{13}\) and \(\tan \theta = -\dfrac{5}{12}\), find \(\sec \theta\).

9 Trig Identity Rewrite · Level 2

Express \(\tan \theta\) in terms of \(\sec \theta\) for \(\theta\) in Quadrant II.

10 Application - Ladder · Level 2

The base of the ladder in the figure is 6 ft from the building, and the angle formed by the ladder and the ground is \(73°\). How high up the building does the ladder touch?

11 Express Theta in Terms of x · Level 2

Express \(\theta\) in each figure in terms of \(x\).

12 Inverse Trig Composition · Level 2

Find the exact value of \(\cos\left(\tan^{-1} \dfrac{9}{40}\right)\).

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