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

Answer:

  r ≈ 13.01

Step-by-step 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

_____

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

Answer 2

Answer:

r = 13.01

Step-by-step explanation:

The formula to find r is  $r=\sqrt{x^2+y^2}$

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:

$tan\theta=\frac{y}{x}$ so

$tan(67.4)=\frac{y}{5.00}$ and

5.00 tan(67.4) = y so

y = 12.01

Now use that in your formula to find r:

$r=\sqrt{(5.00)^2+(12.01)^2}$ and

$r=\sqrt{25+144.2401}$ so

r = 13.01