Question

Choose the correct options for $\sin {630}^{\circ }\&\cos {810}^{\circ }.$

• A. $\cos {810}^{\circ }=0$
• B. $\sin {630}^{\circ }=1$
• C. $\sin {630}^{\circ }=-1$
• D. $\cos {810}^{\circ }=1$

Answer 1

Answer: (A), (C)

$\sin {630}^{\circ }=-1$

Given $\sin {630}^{\circ }\&\cos {810}^{\circ }.$
Now, we can write ${630}^{\circ }={360}^{\circ }+{270}^{\circ }$
Graphically, we can represent it as:

Here, the angle is representing negative $y-$ axis
$\Rightarrow P(\cos \theta ,\sin \theta )\equiv (0,-1)$
Or $P(\cos {630}^{\circ },\sin {630}^{\circ })\equiv (0,-1)$
Comparing: $\sin {630}^{\circ }=-1$

Similarly, let's do the same for $\cos {810}^{\circ }$
Now, ${810}^{\circ }=2\times {360}^{\circ }+{90}^{\circ }$
Graphically, this can be represented as:

$\Rightarrow P(\cos \theta ,\sin \theta )\equiv (0,1)$
Or $P(\cos {810}^{\circ },\sin {810}^{\circ })\equiv (0,1)$
Comparing: $\cos {810}^{\circ }=0$