Trigonometry/Collection of Problems/Trigonometric Functions of Angles

Standard Position of Angles

Sketch each of the following angles in standard position, and state whether it is a first-, second-, third-, or fourth-quadrant angle.

 1. ${\displaystyle 30^{\circ }}$ 2. ${\displaystyle 160^{\circ }}$ 3. ${\displaystyle -80^{\circ }}$ 4. ${\displaystyle 370^{\circ }}$ 5. ${\displaystyle 700^{\circ }}$ 6. ${\displaystyle -110^{\circ }}$ 7. ${\displaystyle 220^{\circ }}$ 8. ${\displaystyle 400^{\circ }}$

Each of the angles ${\displaystyle \theta }$ and ${\displaystyle \phi }$ are in standard position. Are they coterminal?

 9. ${\displaystyle \theta =40^{\circ }\phi =400^{\circ }}$ 10. ${\displaystyle \theta =200^{\circ }\phi =-160^{\circ }}$ 11. ${\displaystyle \theta =-290^{\circ }\phi =-70^{\circ }}$ 12. ${\displaystyle \theta =-290^{\circ }\phi =70^{\circ }}$ 13. ${\displaystyle \theta =110^{\circ }\phi =-290^{\circ }}$ 14. ${\displaystyle \theta =210^{\circ }\phi =-510^{\circ }}$

Values of Trigonometric Functions

In each of the figures find the values of ${\displaystyle \cos \theta }$, ${\displaystyle \sin \theta }$, and ${\displaystyle \tan \theta }$:

1.

2.

3.

4.

5.

6.