Notes:

      MAT129 Fall 2024 Notes

Monday  November 18	Topics:	Using, Solving, and Verifying Trigonometric Identities

9.1 - pg 696, Learning Objectives

* Verify the fundamental trigonometric identities.

Fundamental Identities

Oscar, Unit Circle on 10.30.d.gif

Cofunction identities

The function of an angle is equal to the cofunction of its complement.

complement on 10.28.a.gif

complement, supplement gsp   -- just complementary & supplementary angles

Even-odd Identities

picture the graphs of the functions on 11.04.c.gif

sine and tangent are odd so: f(-x) = - f(x)

cosine is even so: f(-x) = f(x)

Reciprocal Identities 11.04.d.gif

Quotient Identities

tan(A) = sin(A) / cos(A)

cot(A) = cos(A) / sin(A)

oscar

similar figures

Pythagorean Identities Pythagorean Trig Identities

sine-cosine, sin²(A) + cos²(A) = 1     pyth1.gif

tangent-secant, tan²(A) + 1 = sec²(A)     pyth2.gif

cotangent-cosecant, cot²(A) + 1 = csc²(A)     pyth3.gif

Unit Circle and Identities

unitSinCosTriangle gsp   -- sine & cosine functions with a unit circle

unitTanSec gsp   -- tangent & secant functions with a unit circle

unitCotCsc gsp   -- cotangent & cosecant functions with a unit circle

unitfx gsp   -- 6 functions with a unit circle

Pythagorean gsp   -- using only figure to adjust angle

PythagorIdentities gsp   -- using either figure or parameter theta to adjust angle

 

More to Come on Another Day

Sum and Difference Identities

Double-Angle Formulas

Half-Angle formulas

Reduction Formulas

Product-to-Sum Formulas

Sum-to-Product Formulas

 

* Simplify trigonometric expressions using algebra and the identities.

© 11/17/2024, A2 http://www.mathnstuff.com/math/precalc/129/M.11.18.htm