TRIGONOMETRIC FUNCTIONS Let t be a real number and let ( ) = P x y , be the point on the unit circle that corresponds to t. = = = ≠ t y t x t y x x sin cos tan , 0 = ≠ = ≠ = ≠ t y y t x x t x y y csc 1 , 0 sec 1 , 0 cot , 0 TRIGONOMETRIC IDENTITIES Even-Odd Identities θ θ θ θ ( ) ( ) − = − − = − sin sin csc csc θ θ θ θ ( ) ( ) − = − = cos cos sec sec tan tan cot cot θ θ θ θ ( ) ( ) − = − − = − Product-to-Sum Formulas sin sin cos cos 1 2 α β α β α β ( ) ( ) [ ] = − − + cos cos cos cos 1 2 α β α β α β ( ) ( ) [ ] = − + + sin cos sin sin 1 2 α β α β α β ( ) ( ) [ ] = + + − Sum and Difference Formulas α β α β α β ( ) + = + sin sin cos cos sin α β α β α β ( ) − = − sin sin cos cos sin α β α β α β ( ) + = − cos cos cos sin sin α β α β α β ( ) − = + cos cos cos sin sin α β α β α β ( ) + = + − tan tan tan 1 tan tan α β α β α β ( ) − = − + tan tan tan 1 tan tan Sum-to-Product Formulas α β α β α β + = + − sin sin 2 sin 2 cos 2 α β α β α β − = − + sin sin 2 sin 2 cos 2 α β α β α β + = + − cos cos 2cos 2 cos 2 α β α β α β − = − + − cos cos 2sin 2 sin 2 SOLVING TRIANGLES c a b C B A Law of Sines = = A a B b c c sin sin sin Law of Cosines = + − a b c bc A 2 cos 2 2 2 = + − b a c ac B 2 cos 2 2 2 = + − c a b ab C 2 cos 2 2 2 x – 4 – 3 – 6 (1, 0) (0, 1) (0, 1) ( 1, 0) 0, 2p – 2 3p –– 2 7p –– 4 3p –– 4 5p –– 6 7p –– 6 11p ––– 6 4p –– 3 5p –– 3 2p –– 3 5p –– 4 3308 3008 2408 2108 1508 308 1208 608 908 2708 08, 3608 1808 3158 2258 1358 458 y 1 – 2 ( ) , –– 2 3 1 – 2 ( ) , –– 2 3 1 – 2 ( ) , –– 2 3 1 – 2 ( ) , –– 2 3 1 – 2 ( ) , –– 2 3 1 – 2 ( ) , –– 2 3 ( ) , –– 2 2 –– 2 2 ( ) , –– 2 2 –– 2 2 1 – 2 ) , –– 2 3 ( 1 – 2 ) , –– 2 3 ( ( ) , –– 2 2 –– 2 2 ( ) , –– 2 2 –– 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 p p p p p y x t 0 s 5t units t units u 5 t radians P 5 (x, y) x2 1 y2 5 1 0 y x t |t | units s 5 |t | units P 5 (x, y) u 5 t radians x2 1 y2 5 1 Fundamental Identities tan sin cos cot cos sin θ θ θ θ θ θ = = csc 1 sin sec 1 cos cot 1 tan θ θ θ θ θ θ = = = θ θ + = sin cos 1 2 2 θ θ + = tan 1 sec 2 2 θ θ + = cot 1 csc 2 2 Half-Angle Formulas sin 2 1 cos 2 θ θ = ± − cos 2 1 cos 2 θ θ = ± + θ θ θ = − tan 2 1 cos sin Double-Angle Formulas θ θ θ ( ) = sin 2 2sin cos θ θ θ ( ) = − cos 2 cos sin 2 2 θ θ ( ) = − cos 2 2cos 1 2 θ θ ( ) = − cos 2 1 2sin2 θ θ θ ( ) = − tan 2 2tan 1 tan2
RkJQdWJsaXNoZXIy NjM5ODQ=