Key Concepts & Glossary

Key Equations

Cofunction Identities cost=sin(π2−t)sint=cos(π2−t)tant=cot(π2−t)cott=tan(π2−t)sect=csc(π2−t)csct=sec(π2−t)

Key Concepts

  • We can define trigonometric functions as ratios of the side lengths of a right triangle.
  • The same side lengths can be used to evaluate the trigonometric functions of either acute angle in a right triangle.
  • We can evaluate the trigonometric functions of special angles, knowing the side lengths of the triangles in which they occur.
  • Any two complementary angles could be the two acute angles of a right triangle.
  • If two angles are complementary, the cofunction identities state that the sine of one equals the cosine of the other and vice versa.
  • We can use trigonometric functions of an angle to find unknown side lengths.
  • Select the trigonometric function representing the ratio of the unknown side to the known side.
  • Right-triangle trigonometry permits the measurement of inaccessible heights and distances.
  • The unknown height or distance can be found by creating a right triangle in which the unknown height or distance is one of the sides, and another side and angle are known.

Glossary

adjacent side
in a right triangle, the side between a given angle and the right angle
angle of depression
the angle between the horizontal and the line from the object to the observer’s eye, assuming the object is positioned lower than the observer
angle of elevation
the angle between the horizontal and the line from the object to the observer’s eye, assuming the object is positioned higher than the observer
opposite side
in a right triangle, the side most distant from a given angle
hypotenuse
the side of a right triangle opposite the right angle