Precalculus by Richard Wright

But the things that come out of a person’s mouth come from the heart, and these defile them. Matthew 15:18 NIV

Take this test as you would take a test in class. When you are finished, check your work against the answers. On this assignment round your answers to three decimal places unless otherwise directed.

- Sketch the following angles in standard position.

- 135°
- \(\frac{11π}{6}\)
- \(\frac{π}{2}\)
- 4.5

- Find two coterminal angles—one positive and one negative—of a) \(\frac{2π}{3}\) and b) 420°
- Convert to the other angle unit. a) 120° b) 15° c) \(\frac{4π}{3}\) d) \(\frac{π}{10}\)
- Find the reference angle in radians. a) \(\frac{5π}{3}\) b) \(\frac{π}{4}\) c) \(\frac{3π}{4}\)
- Using the unit circle or special right triangles, evaluate the following. a) \(\cos \frac{π}{3}\) b) \(\tan \frac{3π}{2}\) c) \(\csc \frac{5π}{6}\) d) sec
*π* - A point on a angle
*α*is (3, 7). Evaluate a) sin*α*b) cos*α*c) tan*α*d) sec*α*. - Given that \(\sin β = \frac{4}{5}\) and
*β*is an acute angle, find a) cos*β*and b) cot*β*. - Given that \(\tan θ = −\frac{\sqrt{3}}{3}\) and cos
*θ*> 0; a) what quadrant does*θ*lie in? b) Evaluate sec*θ*and c) sin*θ*. - Consider \(y = 2 \sin\left(πx − \frac{π}{2}\right)\). a) Find the amplitude. b) Find the period. c) Find the phase shift.
- Find a function to model this graph.

- Find the exact value of \(\cos\left(\sin^{−1} \frac{3}{4}\right)\).
- Find the exact value of \(\arcsin\left(\cos π\right)\)
- A ship is 10 miles north and 20 miles east of its destination. How far and at what bearing should it sail? (Round to 1 decimal place and use degrees.)
- A mass is bouncing on the end of a spring. If its height at
*t*= 0 is 5 cm above equilibrium and it returns to the highest point after 3 seconds, write a function to model the height from equilibrium. - Use the right triangle to evaluate

- cot
*α*. - sin
*α*. - sec
*α*. *α*(in degrees).

- cot

- \(\frac{8π}{3}, −\frac{4π}{3}\); 60°, −300°
- \(\frac{2π}{3}\); \(\frac{π}{12}\); 240°; 18°
- \(\frac{π}{3}; \frac{π}{4}; \frac{π}{4}\)
- \(\frac{1}{2}\); undefined; 2; −1
- \(\frac{7\sqrt{58}}{58}; \frac{3\sqrt{58}}{58}; \frac{7}{3}; \frac{\sqrt{58}}{3}\)
- \(\frac{3}{5}; \frac{3}{4}\)
- IV; \(\frac{2\sqrt{3}}{3}\); \(−\frac{1}{2}\)
- 2; 2; \(\frac{1}{2}\)
- \(y = \frac{1}{2}\sec\left(2πx\right)\)
- \(\frac{\sqrt{7}}{4}\)
- \(−\frac{π}{2}\)
- 22.4 miles at W 26.6° S
- \(y = 5\cos\left(\frac{2π}{3}t\right)\)
- \(\frac{5\sqrt{11}}{11}; \frac{\sqrt{11}}{6}; \frac{6}{5}; 33.6°\)