Find the values of all trigonometric functions of 135

Question:

Find the values of all trigonometric functions of 135

 

 

Solution:

$\sin 135^{\circ}=\sin \left(180^{\circ}-45^{\circ}\right)$.............. .(using $\sin \left(180^{\circ}-x\right)=\sin x$ )

$=\sin 45^{\circ} \Rightarrow \frac{1}{\sqrt{2}}$

$\operatorname{Cos} 135^{\circ}=\cos \left(180^{\circ}-45^{\circ}\right)$ ...................$. .\left(\right.$ using $\left.\cos \left(180^{\circ}-x\right)=-\cos x\right)$

$=\cos 45^{\circ} \Rightarrow-\frac{1}{\sqrt{2}}$

$\operatorname{Tan} 135^{\circ}=\frac{\sin 135^{\circ}}{\cos 135^{\circ}} \Rightarrow \frac{1 / \sqrt{2}}{-1 / \sqrt{2}}=-1$

$\operatorname{cosec} 135^{\circ}=\frac{1}{\sin 135^{\circ}} \Rightarrow \sqrt{2}$

$\sec 135^{\circ}=\frac{1}{\cos 135^{\circ}} \Rightarrow-\sqrt{2}$

$\cot 135^{\circ}=\frac{1}{\tan 135^{\circ}} \Rightarrow-1$

 

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