Identitas Trigonometri

Matematika adalah bahasa dari fisika. Jadi terkadang mengerjakan soal fisika ketemu aturan hitungan di matematika. Ada beberapa aturan perhitungan di matematika yang dipakai di fisika misal logaritma, turunan, integral, trigonometri dan masih banyak lagi. Pada laman ini saya sajikan aturan identitas trigonometeri yang dipakai di fisika.

Hafalin dulu tabel trigonometeri

Kuadran I, II, III, dan IV

Identitas trigonometri yang sering dipakai di Fisika.

01. $\frac{1}{sin\, \alpha }=cosec\, \, \alpha$

02. $\frac{1}{cos\, \alpha }=sec\, \, \alpha$

03. $\frac{sin\, \alpha}{cos\, \alpha }=tan\, \, \alpha$

04. $\frac{cos\, \alpha}{sin\, \alpha }=cotan\, \, \alpha$

05. $\frac{1}{tan\, \alpha }=cotan\, \, \alpha$

06. $sin^{2}\, \, \alpha +cos^{2}\, \, \alpha=1$

07. $sec^{2}\, \, \alpha=1+tan^{2}\, \, \alpha$

08. $cosec^{2}\, \, \alpha=1+cotan^{2}\, \, \alpha$

09. $sin\, \, 2\alpha=2sin\, \alpha \, cos\, \alpha$

10. $cos\, \, 2\alpha=2cos^{2}\, \alpha \, -1=1-2sin^{2}\, \alpha$

11. $2cos\, \, \alpha\, sin\, \beta =sin\left ( \alpha +\beta \right )-\,sin \left ( \alpha -\beta \right )$

12. $2cos\, \, \alpha\, cos\, \beta =sin\left ( \alpha +\beta \right )+\,cos \left ( \alpha -\beta \right )$

13. $2sin\, \, \alpha\, cos\, \beta =sin\left ( \alpha +\beta \right )+\,sin \left ( \alpha -\beta \right )$

14. $-2cos\, \, \alpha\, cos\, \beta =cos \left ( \alpha +\beta \right )-\,cos \left ( \alpha -\beta \right )$

15. $sin^{2}\, \alpha =\frac{1}{2}-\frac{1}{2}cos\, 2\alpha$

16. $cos^{2}\, \alpha =\frac{1}{2}+\frac{1}{2}cos\, 2\alpha$

17. $sin\, \alpha +cos\beta =2sin\frac{1}{2}\left ( \alpha +\beta \right )cos \frac{1}{2}\left ( \alpha -\beta \right )$

18. $sin\, \alpha -cos\beta =2cos\frac{1}{2}\left ( \alpha +\beta \right )sin\frac{1}{2}\left ( \alpha -\beta \right )$

19. $cos\, \alpha +cos\beta =2cos\frac{1}{2}\left ( \alpha +\beta \right )sin\frac{1}{2}\left ( \alpha -\beta \right )$

20. $cos\, \alpha -cos\beta =-2sin\frac{1}{2}\left ( \alpha +\beta \right )sin\frac{1}{2}\left ( \alpha -\beta \right )$

21. $tan\, \left ( \alpha +\beta \right )=\frac{tan\alpha +tan\beta }{1-tan\, \alpha \, . tan\, \beta }$

22. $tan\, \left ( \alpha -\beta \right )=\frac{tan\alpha -tan\beta }{1+tan\, \alpha \, . tan\, \beta }$

Sudut Rangkap

$sin\, 2\alpha =2sin\alpha \, cos\alpha$
$cos\, 2\alpha =cos^{2}\alpha \, -sin^{2}\alpha$
$cos\, 2\alpha =cos^{2}\alpha \, -1$
$cos\, 2\alpha =1-sin^{2}\alpha \,$
$tan\, 2\alpha =\frac{2tan\, \alpha }{1-tan^{2}\alpha }$

Jumlah dan Selisih Dua Sudut

$sin\left ( A+B \right )=sin A\, cosB+cosA\, sinB$
$sin\left ( A-B \right )=sin A\, cosB-cosA\, sinB$
$cos\left ( A+B \right )=cos A\, cosB-sinA\, sinB$
$cos\left ( A-B \right )=cos A\, cosB+sinA\, sinB$
$tan\left ( A+B \right )=\frac{tanA+tanB}{1-tanA\, tan B}$
$tan\left ( A-B \right )=\frac{tanA-tanB}{1+tanA\, tan B}$

Sudut Tengahan

$cos\left ( \frac{\theta }{2} \right )=\pm \sqrt{\frac{1+cos\theta }{2}}$
$sin\left ( \frac{\theta }{2} \right )=\pm \sqrt{\frac{1-cos\theta }{2}}$
$tan\left ( \frac{\theta }{2} \right )=\pm \sqrt{\frac{1-cos\theta }{1+cos\theta }}$
$tan\left ( \frac{\theta }{2} \right )=\frac{sin\, \theta }{1+cos\, \theta }$
$tan\left ( \frac{\theta }{2} \right )=\frac{ 1-cos\, \theta }{sin\, \theta }$

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Identitas Trigonometri

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