Single Choice

The angle made by line $$r[cos \theta - \sqrt{3} sin \theta ]=5$$ with initial line is

A$$30^{\circ}$$
Correct Answer
B$$45^{\circ}$$
C$$60^{\circ}$$
D$$90^{\circ}$$

Solution

Given equation
$$r[cos \theta - \sqrt{3} sin \theta ]=5$$
$$x-\sqrt{3}y=5$$
Slope of the line is $$\tan\theta=\frac{1}{\sqrt{3}}$$
$$\Rightarrow \theta={30}^{0}$$
Hence, the line makes an angle of $$30^{0}$$ with the initial line.

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