Question

Find the $270$ degrees value for all the trigonometric angles.

Answer 1

Evaluate the given degree value for all trigonometric angles

Let the given degree be $\theta =270°$

So, the value of $\theta$ for all trigonometric angles is as follows,

$$\begin{gathered} \Rightarrow \sin 270°=\sin (3\times \frac{\mathrm{\pi }}{2}+0)\left[\frac{\pi }{2}=90°\right] \\ \sin 270°=-\cos 0° \\ \sin 270°=-1\left[cos0°=1\right] \end{gathered}$$

$$\begin{gathered} \Rightarrow \cos 270°=\cos (3\times \frac{\mathrm{\pi }}{2}+0) \\ \cos 270°=\sin 0° \\ \cos 270°=0\left[sin0°=0\right] \end{gathered}$$

$$\begin{gathered} \Rightarrow \tan 270°=\tan (3\times \frac{\mathrm{\pi }}{2}+0) \\ \tan 270°=-cot0° \\ \tan 270°=-\frac{\cos 0°}{\sin 0°} \\ \tan 270°=-\frac{1}{0} \\ \tan 270°=\mathrm{Not}\mathrm{defined} \end{gathered}$$

$$\begin{gathered} \Rightarrow csc270°=\frac{1}{\sin 270°} \\ csc270°=-\frac{1}{1}\left[sin270°=-1\right] \\ csc270°=-1 \end{gathered}$$

$$\begin{gathered} \Rightarrow sec270°=\frac{1}{\cos 270°} \\ sec270°=\frac{1}{0}\mathbf{}\left[cos270°=0\right] \\ sec270°=\mathrm{Not}\mathrm{defined} \end{gathered}$$

$$\begin{gathered} \Rightarrow cot270°=\frac{\cos 270°}{\sin 270°} \\ cot270°=-\frac{0}{1} \\ cot270°=0 \end{gathered}$$

Hence, the value of trigonometric angles when $\theta =270°$ are:

$$\begin{gathered} \sin \left(270°\right)=-1 \\ \cos \left(270°\right)=0 \\ \tan \left(270°\right)=\mathrm{Not}\mathrm{defined} \\ \csc \left(270°\right)=-1 \\ \sec \left(270°\right)=\mathrm{Not}\mathrm{defined} \\ \cot \left(270°\right)=0 \end{gathered}$$