Siinus - taandamisvalemid (0)

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Trigonomeetria taandamisvalemid

Matemaatika ­ Trigonomeetria taandamisvalemid TAANDAMISVALEMID sin = sin(180 - ) = sin cos = cos(180 - ) = - cos tan = tan(180 - ) = - tan sin = sin(180 + ) = - sin cos = cos(180 + ) = - cos tan = tan(180 + ) = tan sin = sin(360 - ) = - sin cos = cos(360 - ) = cos tan = tan(360 - ) = - tan sin(-) = - sin cos(-) = cos tan(-) = - tan VERTIKAALTELJE JUURES TAANDAMINE sin(90 - ) = cos cos(90 - ) = sin tan(90 - ) = cot sin(90 + ) = cos cos(90 + ) = - sin tan(90 + ) = - cot sin(270 - ) = - cos cos(270 - ) = - sin tan(270 - ) = cot sin(270 + ) = - cos cos(270 + ) = sin tan(270 + ) = - cot VALEMID sin2 + cos2 = 1 tan*cot = 1 sin( + )=sin*cos + cos*sin sin( - )=sin*cos - cos*sin cos( + )=cos*cos - sin*sin cos( - )=cos*cos + sin*sin < a2 = b2 + c2 ­ 2bc cos ++-+-+ ---++- sin cos tan 

Matemaatika

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Trigonomeetria taandamisvalemid

http://www.abiks.pri.ee TAANDAMISVALEMID VALEMID sin = sin(180 - ) = sin sin2 + cos2 = 1 cos = cos(180 - ) = - cos tan = tan(180 - ) = - tan sin = sin(180 + ) = - sin tan*cot = 1 cos = cos(180 + ) = - cos sin( + )=sin*cos + cos*sin tan = tan(180 + ) = tan sin( - )=sin*cos - cos*sin sin = sin(360 - ) = - sin cos( + )=cos*cos - sin*sin cos = cos(360 - ) = cos cos( - )=cos*cos + sin*sin tan = tan(360 - ) = - tan sin(-) = - sin < cos(-) = cos tan(-) = - tan a2 = b2 + c2 ­ 2bc cos VERTIKAALTELJE JUURES TAANDAMINE + + - + - + sin(90 - ) = cos - - - + + - cos(90 - ) = sin sin cos tan tan(90 - ) = cot sin(90 + ) = cos cos(90 + ) = - sin tan(90 + ) = - cot sin(270 - ) = - cos cos(270 - ) = - sin 

Matemaatika

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TAANDAMISVALEMID

TAANDAMISVALEMID X-TELJEST I veerand II veerandist I veerandisse Sin(90®-α)=cosα Sin(180®-α)=sin α Cos(90®-α)=sinα Cos(180®- α)= -cosα Tan(90®-α)=cotα Tan(180®-α)= -tanα Sin(π/2-α)=cosα Cot(180®-α)= - cotα Cos(π/2-α)=sinα Sin(π- α)=sin α Tan(π/2-α)=cotα Cos(π- α)= - cos α Tan(π- α)= -tan α II veerandist I veerandisse Cot(π- α)= -cot α Sin(90®+α)=cosα Cos(90®+α)= -sinα III veerandist I veerandisse Tan(90®+α)= -cotα Sin(180®+ α)= -sin α Sin(π/2+α)=cosα Cos(180®+α)= -cosα Cos(π/2+α)= -sinα Tan(180®+α)= tanα Tan(π/2+α)= -cotα Cot(180®+α)=cotα Sin(π+α)= -sinα III veerandist I veerandisse Cos(π+α)= - cosα Sin(270®-α)= -cosα Tan(π+α)=tanα Cos(270®-α)= -sinα Cot(π+α)=cotα Tan(270®-?

Matemaatika

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Nurkade taandamisvalemid

- + + - 0° 30° 45° 60° 90° 180° 270° 360° Sin 0 1 0 -1 0 Cos 1 0 -1 0 1 Tan 0 1 3 - 0 - 0 Cot - 3 1 0 - 0 - 1. Täispöörete eraldamine Sin(+n360°) = sin Cos(+n360°) = cos tan(+n360°) = tan cot(+n360°) = cot 2. Taandamisvalemid II veerandi nurgale Sin(180°-) = sin cos(180°-) = -cos tan(180°-) = -tan 3. Taandamisvalemid III veerandi nurgale Sin(180°+) = -sin cos(180°+) = -cos tan(180°+) = tan 4. Taandamisvalemid IV veerandi nurgale Sin(360°-) = -sin cos(360°-) = cos tan(360°-) = -tan 5. Negatiivse nurga taandamine Sin(-) = -sin Cos(-) = cos Tan(-) = -tan

Matemaatika

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Trigonomeetria valemid

PÕHISEOSED tan cot = 1 sin 2 + cos 2 = 1 + y + - y + - y + sin 1 tan = 1 + tan 2 = cos cos 2 x x x cot = cos 1 + cot 2 = 1 - - - + + - sin sin 2 +sin +cos

Matemaatika

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Trigonomeetria valemileht

2 2 1° = 180 180 1rad = Negatiivse nurga valemid Nurka saab kirja panna järgneval kujul: sin(-) = - sin + 360°, cos(-) = cos 0° < 360° tan(-) = - tan Nurk + 360° ( ) on sama veerandi cot(-) = -cot nurk mis nurk . Taandamisvalemid Kahe nurga summa ja vahe valemid sin( + 360°) = sin sin( + ) = sin cos + cos sin cos( + 360°) = cos sin( - ) = sin cos - cos sin tan( + 360°) = tan cos( - ) = cos cos + sin sin tan + tan tan( + ) = Täiendusnurga valemid 1 - tan tan

Matemaatika

2

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Trigonomeetria valemid

Trigonomeetria Täiendusnurga valemid: Põhivalemid: sin α=cos ( 90 °−α ) ( sin α )2 + ( cos α )2 =1 ehk cot α = 1 cosα=sin ( 90 °−α ) tan α sin 2 α +cos 2 α =1 1 cos α tan α= sin α cot α= tan α=

Trigonomeetria

2

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TRIGO VALEMID

Trigonomeetria Täiendusnurga valemid: Põhivalemid: sin α=cos ( 90 °−α ) ( sin α )2 + ( cos α )2 =1 ehk cot α = 1 cosα=sin ( 90 °−α ) tan α sin 2 α +cos 2 α =1 1 cos α tan α= sin α cot α= tan α=

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