Question

For the diagram shown below for a unit circle, $\theta =$

• A. ${60}^{\circ }$
• B. ${135}^{\circ }$
• C. ${45}^{\circ }$

Answer 1

The correct option is C ${45}^{\circ }$

For the unit circle, we have the diagram as:

Here, the point $P$ is in the first quadrant and has coordinates: $(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}})$
Here, for $\Delta OPQ,$
$\because$ the circle is a unit circle
$\Rightarrow OP=1\text{units}$
Now, We can define either $\sin \theta ,\cos \theta \text{or}\tan \theta$
$\Rightarrow \tan \theta =\frac{PQ}{OQ}=\frac{y-\text{coordinate}}{x-\text{coordinate}}$
$\Rightarrow \tan \theta =\frac{\frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}}}=1$
$\Rightarrow \theta ={45}^{\circ }$