Mega Widya Pratiwi: May 2013

Monday, 13 May 2013

hubungan fungsi trigonometri dan Membuat Program Menghitung Sin Cos Tangen Menggunakan C++

Hubungan fungsi trigonometri

Fungsi dasar:

$\sin A = \frac{a}{c}\,$

$\cos A = \frac{b}{c}\,$

$\tan A = \frac{\sin A}{\cos A}\ = \frac{a}{b}\,$

$\cot A = \frac{1}{\tan A} = \frac{\cos A}{\sin A}\ = \frac{b}{a}\,$

$\sec A = \frac{1}{\cos A}\ = \frac{c}{b}\,$

$\csc A = \frac{1}{\sin A}\ = \frac{c}{a}\,$

Identitas trigonometri

$\sin^2 A + \cos^2 A = 1 \,$

$1 + \tan^2 A = \frac{1}{\cos^2 A} = \sec^2 A\,$

$1 + \cot^2 A = \frac{1}{\sin^2 A} = \csc^2 A \,$

Penjumlahan

$\sin (A + B) = \sin A \cos B + \cos A \sin B \,$

$\sin (A - B) = \sin A \cos B - \cos A \sin B \,$

$\cos (A + B) = \cos A \cos B - \sin A \sin B \,$

$\cos (A - B) = \cos A \cos B + \sin A \sin B \,$

$\tan (A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \,$

$\tan (A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B} \,$

$2 \sin A \times \cos B = \sin (A + B) + \sin (A - B),$

$2 \cos A \times \sin B = \sin (A + B) - \sin (A - B),$

$2 \cos A \times \cos B = \cos (A + B) + \cos (A - B),$

$2 \sin A \times \sin B = - \cos (A + B) + \cos (A - B),$

Rumus sudut rangkap dua

$\sin 2A = 2 \sin A \cos A \,$

$\cos 2A = \cos^2 A - \sin^2 A = 2 \cos^2 A -1 = 1-2 \sin^2 A \,$

$\tan 2A = {2 \tan A \over 1 - \tan^2 A} = {2 \cot A \over \cot^2 A - 1} = {2 \over \cot A - \tan A} \,$

Rumus sudut rangkap tiga

$\sin 3A = 3 \sin A - 4 \sin^3 A \,$

$\cos 3A = 4 \cos^3 A - 3 \cos A \,$

Rumus setengah sudut

$\sin \frac{A}{2} = \pm \sqrt{\frac{1-\cos A}{2}} \,$

$\cos \frac{A}{2} = \pm \sqrt{\frac{1+\cos A}{2}} \,$

$\tan \frac{A}{2} = \pm \sqrt{\frac{1-\cos A}{1+\cos A}} = \frac {\sin A}{1+\cos A} = \frac {1-\cos A}{\sin A} \,$

Berikut ini merupakan contoh program untuk menghitung sin,cos, dan tangen dengan menggunakan bahasa pemrograman C++.

//program menggunakan rumus trigonometri

#include<iostream>

#include<math.h>

#include<conio.h>

#define PI 3.141

using namespace std;

int main()

{

cout << "==========================================="<<endl;

cout << " Menghitung sin,cos, dan tan "<<endl;

cout << "==========================================="<<endl;

double sudutA,sinA,cosA,tanA;

cout << "Masukkan nilai sudut yang akan dihitung";

cout << " A= "; cin>>sudutA;

//cout << " B= "; cin>>sudutB;

sinA = sin(sudutA*PI/180);

cosA = cos(sudutA*PI/180);

tanA = tan(sudutA*PI/180);

cout << "sin A = " << sinA<<endl;

cout << "cos A = " << cosA<<endl;

cout << "tan A = " << tanA<<endl;

getch();

return 0;

}

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