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Chapter 10: Q. 8 (page 701)

Find a polar equation for the line containing the origin that makes an angle of 30 degree with the positive x-axis.

Short Answer

Expert verified

The equation isθ=nπ+π6

Step by step solution

01

Step 1. Given Information

The given data isthe line containing the origin that makes an angle of 30 degree with the positive x-axis.

02

Step 2. Explanation

The equation of a line in slope-form in rectangular Cartesian coordinates is given below, y=mx+c

The line passes through the origin of the coordinate plane and has a slope equal to m=tan30°

The value of c must be obtained first to determine the equation of line.

0=tan(30°)(0)+cc=0

Thus, the equation of line in rectangular cartesian coordinates is x=3y

The equation can be obtained in polar form by substituting x=rcosθ,y=rsinθ, we get,

rcosθ=3(rsinθ)tanθ=13

03

Step 3. Calculation

Now find the value of angle in radian.

tanθ=13tanθ=tanπ6Asweknowthatiftanθ=tanαthenθ=nπ+α⇒θ=nπ+π6

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