Question

Trigonometric functions of $({90}^o+\theta )$ and $(180-\theta )$ and $(180+\theta )$

Answer 1

$(90+\theta )$

$\sin (90+\theta )=\cos \theta$

$\cos (90+\theta )=-\sin \theta$

$\tan (90+\theta )=-\cot \theta$

$\text{cosec}(90+\theta )=\sec \theta$

$\sec (90+\theta )=-\text{cosec}\theta$

$\cot (90+\theta )=-\tan \theta$

$(180-\theta )$

$\sin (180-\theta )=\sin \theta$

$\cos (180-\theta )=-\cos \theta$

$\tan (180-\theta )=-\tan \theta$

$\text{cosec}(180-\theta )=\text{cosec}\theta$

$\sec (180-\theta )=-\sec \theta$

$\cot (180-\theta )=-\cot \theta$

$(180+\theta )$

$\sin (180+\theta )=-\sin \theta$

$\cos (180+\theta )=-\cos \theta$

$\tan (180+\theta )=\tan \theta$

$\text{cosec}(180+\theta )=-\text{cosec}\theta$

$\sec (180+\theta )=-\sec \theta$

$\cot (180+\theta )=\cot \theta$