Question

The rectangular coordinates of a point are (5.00, y) and the polar coordinates of this point are ( r, 67.4°). What is the value of the polar coordinate r in this case?

Answer 1

r = 13.01

Explanation:

The formula to find r is
`r=√(x^2+y^2)`

We know x = 5.00, we need to find y in order to find r. Use the tangent formula with the given angle to solve for y:

`tan\theta=(y)/(x)` so

`tan(67.4)=(y)/(5.00)` and

5.00 tan(67.4) = y so

y = 12.01

Now use that in your formula to find r:

`r=√((5.00)^2+(12.01)^2)` and

`r=√(25+144.2401)` so

r = 13.01

Answer 2

r ≈ 13.01

Explanation:

The mnemonic SOH CAH TOA reminds you that ...

Cos = Adjacent/Hypotenuse

cos(67.4°) = 5.00/r . . . . . . filling in the given values

Solving for r gives ...

r = 5.00/cos(67.4°) ≈ 13.01

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Check your requirements for rounding. We rounded to 2 decimal places because the x-coordinate, 5.00, was expressed using 2 decimal places.