CHAPTER 8
INTRODUCTION TO TRIGONOMETRY
| TRIGONOMETRIC RATIOS | |
| sin A | $$\sin A=\frac{\text{side opposite to }\angle A}{\text{hypotenuse}}=\frac{BC}{AC}$$ |
| cos A | $$\cos A=\frac{\text{side adjacent to }\angle A}{\text{hypotenuse}}=\frac{AB}{AC}$$ |
| tan A | $$\tan A=\frac{\text{side opposite to }\angle A}{\text{side adjacent to }\angle A}=\frac{BC}{AB}$$ |
| cot A | $$\cot A=\frac{\text{side adjacent to }\angle A}{\text{side opposite to }\angle A}=\frac{AB}{BC}$$ |
| sec A | $$\sec A=\frac{\text{hypotenuse}}{\text{side adjacent to }\angle A}=\frac{AC}{AB}$$ |
csc A | $$\csc A =\frac{\text{hypotenuse}}{\text{side opposite to }\angle A}=\frac{AC}{BC}$$ |
| BASIC IDENTITIES | |
| $$\sin A \cdot \csc A = 1$$ $$\cos A \cdot \sec A = 1$$ $$\tan A \cdot \cot A = 1$$ | |
| RECIPROCAL & QUOTIENT IDENTITIES | |
| $$\sin A=\frac{1}{\csc A},\quad \csc A=\frac{1}{\sin A}$$ $$\cos A=\frac{1}{\sec A},\quad \sec A=\frac{1}{\cos A}$$ $$\tan A=\frac{1}{\cot A},\quad \cot A=\frac{1}{\tan A}$$ $$\tan A=\frac{\sin A}{\cos A},\quad \cot A=\frac{\cos A}{\sin A}$$ | |
| PYTHAGOREAN IDENTITIES | |
| $$\sin^2 A+\cos^2 A=1$$ $$\sec^2 A-\tan^2 A=1$$ $$\csc^2 A-\cot^2 A=1$$ | |
| $$\sin^2 A=1-\cos^2 A$$ $$\cos^2 A=1-\sin^2 A$$ $$\sec^2 A=1+\tan^2 A$$ $$\tan^2 A=\sec^2 A-1$$ $$\csc^2 A=1+\cot^2 A$$ $$\cot^2 A=\csc^2 A-1$$ | |
