Trigonometric Functions, Identities & Equations

Special Angles

    \[\begin{array}{|c|c|c|c|c|c|} \hline \theta & 0^{\circ}& 30^{\circ} &  45^{\circ}  &  60^{\circ}  &  90^{\circ} \\ \hline  \sin\theta &  \frac{\sqrt{0}}{2}=0  &  \frac{\sqrt{1}}{2}=\frac{1}{2}  &  \frac{\sqrt{2}}{2}  &  \frac{\sqrt{3}}{2}  &  \frac{\sqrt{4}}{2}=1 \\ \hline  \cos\theta &  \frac{\sqrt{4}}{2}=1  &  \frac{\sqrt{3}}{2}  &  \frac{\sqrt{2}}{2}  &  \frac{\sqrt{1}}{2}=\frac{1}{2}  &  \frac{\sqrt{0}}{2}=0 \\ \hline  \tan\theta &  0  &  \frac{1}{\sqrt{3}}  &  1  &  \sqrt{3}  & - \\ \hline \end{array}\]

Reciprocal Functions
1.\,\text{cosec }\theta=\dfrac{1}{\sin\theta}\$2.\,\sec\theta=\dfrac{1}{\cos\theta}\$
3.\,\cot\theta=\dfrac{1}{\tan\theta}
Negative Functions
1.\,\sin(-\theta)=-\sin\theta
2.\,\cos(-\theta)=\cos\theta
3.\,\tan(-\theta)=-\tan\theta
Tangent & Cotangent
1.\,\tan\theta=\dfrac{\sin\theta}{\cos\theta}\$2.\,\cot\theta=\dfrac{\cos\theta}{\sin\theta}[/stextbox]  [stextbox caption="Trigonometric Identities" stextbox id="download"]1.\,\sin^2{\theta} + \cos^2{\theta} = 12.\,\sec^2{\theta}=1+\tan^2{\theta}3.\,\text{cosec}^2{\theta}=1 + \cot^2{\theta}[/stextbox]  [stextbox caption="Addition Formulae" stextbox id="info"]1.\,\sin(A \pm B) = \sin A\cos B \pm \cos A \sin B2.\,\cos(A \pm B) = \cos A \cos B \mp \sin A \sin B3.\,\tan(A \pm B) = \dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}[/stextbox]  [stextbox caption="Double Angle Formulae" stextbox id="default"]1.\,\sin 2A = 2\sin A \cos A2.\,\cos2A = \cos^2A – \sin^2A= 2 \cos^2A -1= 1 – 2\sin^2A3.\,\tan 2A = \dfrac{2\tan A}{1-\tan^2A}[/stextbox]  [stextbox caption="R-Formulae" stextbox id="download"]Fora > 0, b > 0, 0^\circ < \alpha < 90^\circ,1.\,a\sin \theta \pm b \cos \theta = R \sin (\theta \pm \alpha)2.\,a \cos \theta \pm b \sin \theta = R \cos (\theta \mp \alpha)whereR=\sqrt{a^2+b^2}, \tan\alpha=\dfrac{b}{a}$.
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