How do you convert $(2, \frac{π}{4})$ $(2, pi/4)$ into rectangular coordinates?

Question

How do you convert $(2, \frac{π}{4})$ $(2, pi/4)$ into rectangular coordinates?

2 Answers

Impact of this question

8562 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-18T09:40:14

$x = 2 cos (\frac{π}{4}) = 2 \cdot 0.707 = 1.414$ $x=2cos(pi/4)=2*0.707=1.414$

$y = 2 sin (\frac{π}{4}) = 2 \cdot 0.707 = 1.414$ $y=2sin(pi/4)=2*0.707=1.414$

Rectangular coordinates are (1.4,1.4)

Explanation:

These coordinates describe a line 2 units long, starting at the origin, $(0, 0)$ $(0,0)$ , at an angle of $\frac{π}{4}$ $pi/4$ radians anticlockwise (counterclockwise) from the positive axis.

Some find it easier to work in radians, some in degrees. $\frac{π}{4}$ $pi/4$ is $45^{o}$ $45^o$ . I'll keep working in radians, since that is how the question is set up.

For rectangular coordinates we need to find the distance of the projection along the x-axis for the first point and along the y-axis for the second.

Draw a diagram. It's crucial.

Now use the definition of trigonometry. The two points are as follows:

$x = 2 cos (\frac{π}{4}) = 2 \cdot 0.707 = 1.414$ $x=2cos(pi/4)=2*0.707=1.414$

$y = 2 sin (\frac{π}{4}) = 2 \cdot 0.707 = 1.414$ $y=2sin(pi/4)=2*0.707=1.414$

Answer 2 · 2016-01-18T09:43:55

$(\sqrt{2}, \sqrt{2})$ $( sqrt2 , sqrt2 )$

Explanation:

Using the formulae that links Polar and Cartesian coordinates .

$∙ x = r cos θ$ $• x = rcostheta$

$∙ y = r sin θ$ $• y = rsintheta$

here r = 2 , $θ = \frac{π}{4}$ $theta = pi/4$

$\Rightarrow x = 2 cos (\frac{π}{4}) = 2 . \frac{1}{\sqrt{2}} = \frac{2}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \sqrt{2}$ $rArr x = 2cos(pi/4) = 2 . 1/sqrt2 = 2/sqrt2 xx sqrt2/sqrt2 = sqrt2$

and y = $2 sin (\frac{π}{4}) = 2 . \frac{1}{\sqrt{2}} = \sqrt{2}$ $2sin(pi/4) = 2. 1/sqrt2= sqrt2$

Science

Math

Humanities

... and beyond

How do you convert $(2, \frac{π}{4})$ $(2, pi/4)$ into rectangular coordinates?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you convert (2,π4)(2, pi/4) into rectangular coordinates?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

How do you convert $(2, \frac{π}{4})$ $(2, pi/4)$ into rectangular coordinates?