Trigonometry

Trigonometry Formulas (Dropdown + MathJax)

1. Basic Trigonometric Ratios

\[ \sin\theta = \frac{Opposite}{Hypotenuse} \] \[ \cos\theta = \frac{Adjacent}{Hypotenuse} \] \[ \tan\theta = \frac{Opposite}{Adjacent} \] \[ \cosec\theta = \frac{Hypotenuse}{Opposite} \] \[ \sec\theta = \frac{Hypotenuse}{Adjacent} \] \[ \cot\theta = \frac{Adjacent}{Opposite} \]

2. Reciprocal Identities

\[ \sin\theta = \frac{1}{\cosec\theta} \] \[ \cos\theta = \frac{1}{\sec\theta} \] \[ \tan\theta = \frac{1}{\cot\theta} \] \[ \cosec\theta = \frac{1}{\sin\theta} \] \[ \sec\theta = \frac{1}{\cos\theta} \] \[ \cot\theta = \frac{1}{\tan\theta} \]

3. Quotient Identities

\[ \tan\theta = \frac{\sin\theta}{\cos\theta} \] \[ \cot\theta = \frac{\cos\theta}{\sin\theta} \]

4. Pythagorean Identities

\[ \sin^2\theta + \cos^2\theta = 1 \] \[ 1 + \tan^2\theta = \sec^2\theta \] \[ 1 + \cot^2\theta = \cosec^2\theta \]

5. Co-function Identities

\[ \sin(90^\circ-\theta) = \cos\theta \] \[ \cos(90^\circ-\theta) = \sin\theta \] \[ \tan(90^\circ-\theta) = \cot\theta \] \[ \sec(90^\circ-\theta) = \cosec\theta \]

6. Sum & Difference Formulas

\[ \sin(A\pm B) = \sin A \cos B \pm \cos A \sin B \] \[ \cos(A\pm B) = \cos A \cos B \mp \sin A \sin B \] \[ \tan(A\pm B) = \frac{\tan A \pm \tan B}{1 \mp \tan A \tan B} \]

7. Double Angle Formulas

\[ \sin 2A = 2\sin A \cos A \] \[ \cos 2A = \cos^2A - \sin^2A \] \[ \tan 2A = \frac{2\tan A}{1-\tan^2A} \]

8. Half Angle Formulas

\[ \sin^2\frac{A}{2} = \frac{1-\cos A}{2} \] \[ \cos^2\frac{A}{2} = \frac{1+\cos A}{2} \] \[ \tan\frac{A}{2} = \frac{1-\cos A}{\sin A} \]

9. Standard Angle Values

\[ \sin 30^\circ = \frac{1}{2},\quad \cos 30^\circ = \frac{\sqrt{3}}{2} \] \[ \sin 45^\circ = \frac{1}{\sqrt{2}},\quad \cos 45^\circ = \frac{1}{\sqrt{2}} \] \[ \sin 60^\circ = \frac{\sqrt{3}}{2},\quad \cos 60^\circ = \frac{1}{2} \]

10. Degree–Radian Conversion

\[ \pi\ \text{rad} = 180^\circ \] \[ 1^\circ = \frac{\pi}{180}\text{ rad} \]