Rumus-Rumus Dasar Trigonometri


\cos (\alpha + \beta) = \cos \alpha \cos \beta- \sin \alpha \sin \beta

\cos (\alpha- \beta) = \cos \alpha \cos \beta + \sin \alpha \sin \beta

\sin (\alpha + \beta) = \sin \alpha \cos \beta + \cos \alpha \sin \beta

\sin (\alpha + \beta) = \sin \alpha \cos \beta- \cos \alpha \sin \beta

\tan (\alpha + \beta) = \dfrac{\tan \alpha + \tan \beta}{1- \tan \alpha \cdot \tan \beta}

\tan (\alpha- \beta) = \dfrac{\tan \alpha- \tan \beta}{1+\tan \alpha \cdot \tan \beta}

.

\sin 2\alpha = 2 \sin \alpha \cos \alpha

\cos 2\alpha = \cos^2 \alpha- \sin^2 \alpha

\cos 2\alpha = 1- 2 \sin^2 \alpha

\cos 2\alpha = 2\cos^2 \alpha- 1

\tan 2\alpha = \dfrac{2\tan \alpha}{1- \tan^2 \alpha}

.

1 + \tan^2 \alpha = \sec^2 \alpha

1 + \cot^2 \alpha = \csc^2 \alpha

.

\sin^2 \alpha = \dfrac{1}{2} (1- \cos 2 \alpha)

\cos^2 \alpha = \dfrac{1}{2} (1 + \cos 2\alpha)

.

\sin \square = \pm \sqrt{\dfrac{1}{2}(1-\cos 2\square)}

\sin \dfrac{1}{2} \square = \pm \sqrt{\dfrac{1}{2}(1-\cos \square)}

\cos \square = \pm \sqrt{\dfrac{1}{2}(1+\cos 2\square)}

\cos \dfrac{1}{2} \square = \pm \sqrt{\dfrac{1}{2}(1+\cos \square)}

.

2 \sin \alpha \cos \beta = \sin (\alpha + \beta) + \sin (\alpha- \beta)

2 \cos \alpha \sin \beta = \sin (\alpha + \beta)- \sin (\alpha- \beta)

2 \cos \alpha \cos \beta = \cos (\alpha + \beta) + \cos (\alpha- \beta)

2 \sin \alpha \sin \beta = -[\cos (\alpha + \beta)- \cos (\alpha- \beta)]

.

\sin \alpha + \sin \beta = 2 \sin \dfrac{1}{2} (\alpha + \beta) \cos \dfrac{1}{2} (\alpha- \beta)

\sin \alpha- \sin \beta = 2 \cos \dfrac{1}{2} (\alpha + \beta) \sin \dfrac{1}{2} (\alpha- \beta)

\cos \alpha + \cos \beta = 2 \cos \dfrac{1}{2} (\alpha + \beta) \cos \dfrac{1}{2} (\alpha- \beta)

\cos \alpha- \cos \beta = -2 \sin \dfrac{1}{2} (\alpha + \beta) \sin \dfrac{1}{2} (\alpha- \beta)

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3 comments on “Rumus-Rumus Dasar Trigonometri

  1. assalamualaikum ka . aku mau nanya boleh kalo ada soal tuh kaya gni ni
    Sin2 1◦ + Sin2 3◦ + Sin2 5◦ +…+ Sin2 87◦+ Sin2 89.
    itu cara.a gimana ka ?
    trimakasih .

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