Right Triangle Trigonometry—Section 6.2—Day 1

PRELIMINARIES:
Similar Triangles
that have corresponding angles of equal measure.  Change one triangle here and see the other remain similar.  Besides having congruent angle measure, the RATIOS of sides of similar triangles stay fixed.

The Pythagorean Theorem advises us that  if  is the hypotenuse of the right triangle with legs  and. This video is a visual proof that for a right triangle, .

Trigonometry: the branch of mathematics that deals with the sides and angles of right triangles, calculations using these relationships, and the functions derived from these relationships.

The Trigonometric Functions     Together, similar triangles and the Pythagorean theorem allow us to relate ratios of sided of a right triangle to measures of angles—

Exactly six ratios can be written using the sides of a right triangle. The ancient Greeks named the six ratios.  The names and abbreviations for these ratios are still used, worldwide, today!

Advise: Study the definition on page 494, do as many problems as you need in the study plan (along with your Math Lab homework) and use this spreadsheet to help you memorize the names of the trig function for each of the six ratios.

Goal: Memorize the names, abbreviations and right triangle ratios for the six trig functions.

The Pythagorean Theorem yields side ratios for 45o- 45o- 90o and 30o- 60o- 90o triangles.  We use these angles and their trig ratios often in solving application problems and to develop other trig ideas throughout this course.

Advise: Study pages 496 and 497 and draw these triangles several times.  Work until you memorize the sine, cosine and tangent ratios for 30o, 45o and 60o angles much as you know the multiplication facts.

Goal: Memorize the six trig values for 30, 45 and 60 degrees.