TRIGONOMETRY Let  Be Any Angle in the Standard Position Right Triangle Definition of Trig Functions and Let P(,) X Y Be a Point on the Terminal Side Of

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TRIGONOMETRY Let  Be Any Angle in the Standard Position Right Triangle Definition of Trig Functions and Let P(,) X Y Be a Point on the Terminal Side Of

Definitions of Trig Functions of Any Angle TRIGONOMETRY Let be any angle in the standard position Right Triangle Definition of Trig Functions and let P(,) x y be a point on the terminal side of . If r is the distance from 0,0 toxy, and r x22 y 0, x 0, y 0 y x y sin , cos , tan r r x opposite a hypotenuse c r r x sin csc csc , sec , cot hypotenuse c opposite a y x y adjacent b hypotenuse c cos sec Reference Angles hypotenuse c adjacent b Let be an angle in standard position. Its reference opposite a adjacent b angle is the acute angle formed by the terminal tan cot adjacent b opposite a side of and the horizontal axis. Degrees to Radians Formulas Example: If x is an angle in degrees and t is an angle in 315 radians then: 360 315 45 t x180 t tx and 180x 180 Sines, Cosines, and Tangents of Special Angles The Signs of Trig Functions Q I Q II Q III Q IV sin + + cos + + tan + + Formulas and Identities sin cos Ratio: tan cot cos sin Reciprocal Identities Even/Odd 1 cos( ) cos Even 0 csc 30 45 60 90 sin sin( ) sin 6 4 3 2 1 Odd sin 0 1 1 tan( ) tan 2 3 sec 2 2 2 cos 1 cos 1 0 cot tan 0 dne tan 3 1 3 3 Pythagorean Identities sin2 cos 2 1 tan 2 1 sec 2 1 cot22 csc TRIGONOMETRY Formulas and Identities Double Angle Formulas Half-Angle Formulas sin(2 ) 2sin cos 1 cos Graphs of Trig Functions sin cos(2 ) cos22 sin 22 yx sin 2 1 cos 2cos 1 cos Domain: x, 22 1 2sin2 Range: y [ 1,1] 1 cos sin 2 tan tan Period: 2 tan(2 ) 2 sin 1 cos 1 tan2 Amplitude: 1 yx cos Cofunction Formulas Domain: sin(90 ) cos cos(90 ) sin Range: Period: sin cos cos sin 22 Amplitude: 1 Sum and Difference Formulas yx tan sin( ) sin cos cos sin Domain: cos( ) cos cos sin sin x and xn tan tan 2 tan( ) 1 tan tan Range: y, Period: Sum to Product Formulas Amplitude: None sin sin 2sin cos 22 yx cot Domain: x and xn sin sin 2cos sin 22 Range: Period: cos cos 2cos cos 22 Amplitude: None cos cos 2sin sin 22 yx sec Domain: Product to Sum Formulas 1 sin sin cos( ) cos( ) 2 Range: 1 cos cos cos( ) cos( ) y ( , 1] [1, ) 2 Period: 2 1 sin cos sin( ) sin( ) Amplitude: None 2 1 cos sin sin( ) sin( ) yx csc 2 Domain: Inverse Trig Functions Range: ysin1 x is equivalent to x sin y , y 22 Period: ycos1 x is equivalent to x cos y , 0 y Amplitude: None ytan1 x is equivalent to x tan y , y 22 .

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