**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—see this animation.

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 **45 ^{o}- 45^{o}- 90^{o} and 30^{o}-
60^{o}- 90^{o} 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 30^{o}, 45^{o} and 60^{o} angles
much as you know the multiplication facts.

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