4.3 | Right Triangle Trigonometry


Let \(\theta\) be an acute angle \((0 < \theta < \pi/2)\) of a right triangle. The six basic trigonometric functions are defined as follows:
  • \(\displaystyle \sin \theta = \frac{opp}{hyp}\)
  • \(\displaystyle \csc \theta = \frac{hyp}{opp}\)
  • \(\displaystyle \cos \theta = \frac{adj}{hyp}\)
  • \(\displaystyle \sec \theta = \frac{hyp}{adj}\)
  • \(\displaystyle \tan \theta = \frac{opp}{adj}\)
  • \(\displaystyle \cot \theta = \frac{adj}{opp}\)

where \(opp\) is the length of the side opposite \(\theta\), \(adj\) is the length of the side adjacent to \(\theta\) and sharing the right angle, and \(hyp\) is the length of the hypotenuse (the side opposite the right angle).

E 4.3 Exercises