4.3 - R IGHT T RIANGLE T RIGONOMETRY

I N THIS SECTION, YOU WILL LEARN TO :  Evaluate trigonometric functions of acute angles  Use fundamental trigonometric identities  Use a calculator to evaluate trigonometric functions

S IX T RIGONOMETRIC F UNCTIONS OF A R IGHT T RIANGLE :  Use SOH CAH TOA to remember all six of the trigonometric functions:

E XAMPLE : 12

A NSWERS : Use the Pythagorean Theorem to find the hypotenuse: 6 12

S PECIAL R IGHT T RIANGLES :

S IX TRIGONOMETRIC VALUES OF THE SPECIAL RIGHT TRIANGLES : * Note that certain sine and cosine angles are equal.

C OFUNCTIONS OF COMPLEMENTARY ANGLES ARE CONGRUENT : Sine-Cosine, Tangent-Cotangent, and Secant-Cosecant are cofunctions.

E XAMPLE OF COMPLEMENTARY ANGLES : Use the given function values and the cofunction relationships to find the indicated trigonometric functions.

ANSWERS:

F UNDAMENTAL T RIGONOMETRIC I DENTITIES : A) Reciprocal Identities :

F UNDAMENTAL T RIGONOMETRIC I DENTITIES : B) Quotient Identities:

F UNDAMENTAL T RIGONOMETRIC I DENTITIES : C) Pythagorean Identities:

P ROOF OF THE S INE P YTHAGOREAN I DENTITY : Prove:

E XAMPLES :

A NSWERS :

E XAMPLES : 2) Use trigonometric identities to transform the left side of the equation into the right side.

A NSWERS :

C ALCULATOR E XAMPLES :

A NSWERS : :

C ALCULATOR E XAMPLES :

A NSWERS :