Karta wzoro w trygonometrycznych

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Karta wzoro w trygonometrycznych

𝛼 0/0^° 𝜋

6/30^° 𝜋

4/45^° 𝜋

3/60^° 𝜋

2/90^°

sin 𝛼 0 1

2

√2 2

√3

2 1

cos 𝛼 1 √3

2

√2 2

1

2 0

tg 𝛼 0 √3

3 1 √3 −

ctg 𝛼 − √3 1 √3

3 0

sin(𝜋 − 𝛼) = sin 𝛼 sin(−𝛼) = −sin 𝛼 sin(𝛼 + 𝜋) = −sin 𝛼 sin(𝛼 + 2𝑘𝜋) = sin 𝛼 cos(𝜋 − 𝛼) = − cos 𝛼 cos(−𝛼) = cos 𝛼 cos(𝛼 + 𝜋) = −cos 𝛼 cos(𝛼 + 2𝑘𝜋) = cos 𝛼

tg (−𝛼) = −tg 𝛼 tg (𝛼 + 𝑘𝜋) = tg 𝛼

ctg (−𝛼) = −ctg 𝛼 ctg (𝛼 + 𝑘𝜋) = ctg 𝛼

sin (𝜋

2− 𝛼) = cos 𝛼 cos (𝜋

2− 𝛼) = sin 𝛼 tg (𝜋

2− 𝛼) = ctg 𝛼 ctg (𝜋

2− 𝛼) = tg 𝛼

𝐭𝐠 𝜶 =^{𝐬𝐢𝐧 𝜶}

𝐜𝐨𝐬 𝜶 𝐜𝐭𝐠 𝜶 =^{𝐜𝐨𝐬 𝜶}

𝐬𝐢𝐧 𝜶= ^𝟏

𝐭𝐠 𝜶 𝐜𝐨𝐬^𝟐𝜶 + 𝐬𝐢𝐧^𝟐𝜶 = 𝟏

sin(𝛼 + 𝛽) = sin 𝛼 cos 𝛽 + cos 𝛼 sin 𝛽 cos(𝛼 + 𝛽) = cos 𝛼 cos 𝛽 −sin 𝛼 sin 𝛽 sin(𝛼 − 𝛽) = sin 𝛼 cos 𝛽 − cos 𝛼 sin 𝛽 cos(𝛼 − 𝛽) = cos 𝛼 cos 𝛽 +sin 𝛼 sin 𝛽 𝐬𝐢𝐧 𝟐𝜶 = 𝟐 𝐬𝐢𝐧 𝜶 𝐜𝐨𝐬 𝜶 𝐜𝐨𝐬 𝟐𝜶 = 𝐜𝐨𝐬^𝟐𝜶 − 𝐬𝐢𝐧^𝟐𝜶 =

= 𝟐𝐜𝐨𝐬^𝟐𝜶 − 𝟏 = 𝟏 − 𝟐𝐬𝐢𝐧^𝟐𝜶

sin 𝛼 + sin 𝛽 = 2 sin^𝛼+𝛽₂ cos^𝛼−𝛽₂ sin 𝛼 − sin 𝛽 = 2 cos^𝛼+𝛽₂ sin^𝛼−𝛽₂

cos 𝛼 + cos 𝛽 = 2 cos^𝛼+𝛽

2 cos^𝛼−𝛽

2 cos 𝛼 − cos 𝛽 = −2 sin^𝛼+𝛽

2 sin^𝛼−𝛽

2