Todas as fórmulas trigonométricas importantes para cálculos/exercícios matemáticos:
- [tex] \sin^2 \theta + \cos^2 \theta = 1 [/tex]
- $$ \sin^2 \theta + \cos^2 \theta = 1 $$
- $$ \tan \theta = \dfrac{ \sin \theta }{ \cos \theta } $$
- $$ \tan \theta = \dfrac{1}{ \tan (90^{\circ}- \theta )} $$
- $$ \sin (- \theta ) = - \sin \theta $$
- $$ \cos (- \theta ) = \cos \theta $$
- $$ \tan ( - \theta ) = - \tan \theta $$
- $$ \sin ( 90^{\circ} - \theta ) = \cos \theta $$
- $$ \cos ( 90^{\circ} - \theta ) = \sin \theta $$
- $$ \sin ( 180^{\circ} - \theta ) = \sin \theta $$
- $$ \cos ( 180^{\circ} - \theta ) = - \cos \theta $$
- $$ \sin ( 180^{\circ} + \theta ) = - \sin \theta $$
- $$ \cos ( 180^{\circ} + \theta ) = - \cos \theta $$
- $$ \sin ( 360^{\circ} - \theta ) = - \sin \theta $$
- $$ \cos (360^{\circ} - \theta ) = \cos \theta $$
- $$ \sin ( \theta \pm \delta ) = ( \sin \theta )( \cos \delta) \pm ( \sin \delta )( \cos \theta ) $$
- $$ \cos ( \theta \pm \delta ) = ( \cos \theta )(\cos \delta) \mp ( \sin \theta ) ( \sin \delta) $$
- $$ \tan ( \theta \pm \delta ) = \dfrac{ ( \tan \theta ) \pm ( \tan \delta ) }{1 \mp ( \tan \theta )( \tan \delta ) } $$
- $$ \sin \dfrac{ \theta }{2} = \sqrt{ \dfrac{ 1 - \cos \theta }{2} } $$
- $$ \cos \dfrac{ \theta }{2} = \sqrt{ \dfrac{1+ \cos \theta }{2} } $$
- $$ \tan \dfrac{ \theta }{2} = \sqrt{ \dfrac{1 - \cos \theta }{1 + \cos \theta } }$$ $$= \dfrac{ \sin \theta }{1+ \cos \theta } = $$ $$ \dfrac{ \sqrt{ \tan^2 \theta + 1} -1 }{ \tan \theta } $$
- $$ \sin ( 2 \theta ) = 2( \sin \theta ) ( \cos \theta ) $$
- $$ \cos ( 2 \theta ) = \cos^2 \theta - \sin^2 \theta = 2 \cos^2 \theta - 1 $$
- $$ \tan ( 2 \theta ) = \dfrac{ 2 \tan \theta }{ 1 - \tan^2 \theta} $$
- $$ \sin (3 \theta ) = 3 \sin \theta - 4 \sin^3 \theta $$
- $$ \cos (3 \theta ) = 4 \cos^3 \theta - 3 \cos \theta $$
- $$ \tan (3 \theta ) = \dfrac{ \tan^2 \theta - 3 \tan \theta }{ 3 \tan^2 \theta - 1 } $$
- $$ \sin \theta + \sin \delta = 2 \left( \sin \dfrac{ \theta + \delta}{2} \right) \left( \cos \dfrac{ \theta - \delta}{2} \right) $$
- $$ \sin \theta - \sin \delta = 2 \left( \sin \dfrac{ \theta - \delta}{2} \right) \left( \cos \dfrac{ \theta + \delta}{2} \right) $$
- $$ \cos \theta + \cos \delta = 2 \left( \cos \dfrac{ \theta + \delta}{2} \right) \left( \cos \dfrac{ \theta - \delta}{2} \right) $$
- $$ \cos \theta - \cos \delta = -2 \left( \sin \dfrac{ \theta + \delta}{2} \right) \left( \sin \dfrac{ \theta - \delta}{2} \right) $$
- $$ \tan \theta + \tan \delta = \dfrac{ \sin ( \theta + \delta) }{( \cos \theta )( \cos \delta ) } $$
- $$ \tan \theta - \tan \delta = \dfrac{ \sin ( \theta - \delta) }{( \cos \theta )( \cos \delta) } $$
- $$ ( \cos \theta + i \sin \theta)^n= \cos (n \theta) + i \sin (n \theta) $$
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