Trigonometrical Ratios of Allied Angles
Category : JEE Main & Advanced
Two angles are said to be allied when their sum or difference is either zero or a multiple of \[{{90}^{o}}\].
| Allied angles \[\to \] | \[\sin \theta \] | \[cos\theta \] | \[tan\theta \] |
| Trigo. Ratio | |||
| \[\downarrow \,\,(-\theta )\] | \[-\sin \theta \] | \[cos\theta \] | \[-tan\theta \] |
| \[(90-\theta )\] or \[\left( \frac{\pi }{2}-\theta \right)\] | \[cos\theta \] | \[\sin \theta \] | \[\cot \,\theta \] |
| \[(90-\theta )\] or \[\left( \frac{\pi }{2}-\theta \right)\] | \[\cos \theta \] | \[-\,\sin \theta \] | \[-\cot \,\theta \] |
| \[(180-\theta )\] or\[(\pi -\theta )\] | \[\sin \theta \] | \[-\,\cos \theta \] | \[-tan\theta \] |
| \[(180+\theta )\] or \[(\pi -\theta )\] | \[-\,\sin \theta \] | \[-\,\cos \theta \] | \[tan\theta \] |
| \[(270-\theta )\]or \[\left( \frac{3\pi }{2}-\theta \right)\] | \[-\,\cos \theta \] | \[-\,\sin \theta \] | \[\cot \,\theta \] |
| \[(270+\theta )\] or \[\left( \frac{3\pi }{2}-\theta \right)\] | \[-\,\cos \theta \] | \[\sin \theta \] | \[-\cot \,\theta \] |
| \[(360-\theta )\] or \[(2\pi -\theta )\] | \[-\,\sin \theta \] | \[cos\theta \] | \[-tan\theta \] |
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