Section 13.1.a Trigonometry

The word trigonometry is derived from the Greek Words- trigon meaning triangle and Metra meaning measurement A B C a b c  In the right triangle the measurement of angle  A is 

Trigonometric Ratios Def: the 3 basic trigonometric ratios are defined for the acute angles in any right triangle a b c A B C For any  A a is opposite to  A b is adjacent to  A c is the hypotenuse For any  B b is opposite to  B a is adjacent to  B c is the hypotenuse

(SOH) (CAH) (TOA) A a c b Find:

A B C a b c  Note: The values of the trigonometric functions do not depend on the size of the triangle For any angle  The ratio of the sides remains constant

1.) A B C Find the 3 basic trig ratios for  A sin A = cos A = tan A =

The reciprocal trigonometric functions: sine  = cosine  = tangent  = cosecant  = secant  = cotangent  = A B C a b c  Soh-Cah-Toa

2.) 6 3 A B C Find all 6 trig ratios for  B Sin B = Cos B = Tan B = Csc B = Sec B = Cot B =

3.) Find the tan A when cos A = 2/3 1st determine the lentgh of the 3rd side x A

Special Triangles 4.) 45 o -45 o -90 o Triangle Isosceles Triangle a a 45 o Use the Pythagorean Theorem to find the length of the hypotenuse a 2 + a 2 = h 2 2a 2 = h 2 a 2 + b 2 = c 2

5.) 45 o -45 o -90 o Triangle find sin 45 o = cos 45 o = tan 45 o =

Special Triangles 6.) 30 o -60 o -90 o Triangle find 1 60 o 2 30 o sin 30 o = cos 60 o = cot 60 o =

Homework Practice 97 worksheet