Trigonometry: The study of triangles (sides and angles) physics surveying Trigonometry has been used for centuries in the study of: astronomy geography engineering

A B C adjacent h y p o t e n u s e opposite

A B C adjacent opposite h y p o t e n u s e

A B C opposite adjacent h y p o t e n u s e

A B C opposite adjacent h y p o t e n u s e

A B C opp adj hyp SOHCAH TOA

A B C op p adj hy p SOH CAH TOA

A B C adj opp hyp SOH CAH TOA

A B C adj opp hy p SOH CAH TOA

sin 21° = cos 53° = tan 72° = Use a calculator to determine the following ratios.

sin A = cos B = tan C =  A = sin -1 (0.4142)  B = cos -1 (0.6820)  C = tan -1 (1.562) = 24° = 47° = 57° Determine the following angles (nearest degree).

Determine the following angles (nearest degree). sin A = cos B = tan C =  A = sin -1 (0.5833)  B = cos -1 (0.2666)  C = tan -1 (1.875) = 36° = 75° = 62° = = = 1.875

A B C a 6 cm Example 1: Determine side a 30º a = 6 sin 30° a = 3 cm a = 6 (0.5) hyp opp SOH CAH TOA

A B C 50º b 9 m 40º Ex. 2: Name two trig ratios that will allow us to calculate side b.

A B C Example 3: Determine side b 55º b 8 cm b = 8 tan 55° b = 11.4 cm b = 8 (1.428) opp ad j SOH CAH TOA

P Q R 12 cm 17 cm Example 4: Determine the measure of  P. cos P =  P = 45.1   P = cos –1 ( ) adjacent hypotenuse SOH CAH TOA

P Q R q 12 cm Example 5: Determine the measure of side PR. q(tan 35°) = 12 q = 17.1 cc m 35  opp adj Method 1

P Q R q 12 cm Example 6: Determine the measure of side PR. q = 12(tan 55°) q = 17.1 cc m 35  opp adj Method 2  Q = 90° – 35°  Q = 55° 55° q = 12(1.428)

Ex. 7: In  PQR,  Q = 90°. a) Find sin R if PR = 8 cm and PQ = 4 cm. R P Q 4 cm 8 cm b) Find cos R. RQ 2 = 8 2 – 4 2 RQ 2 = 64 – 16 RQ 2 = 48