find the cartesian co-ordinate of the point (3,150degree)
r = 3, Ø = 150°
cos150 = x/3
x = 3(-√3/2) = -3√3/2
sin150 = y/3
y = 3sin150 = 3(1/2) = 3/2
the point is (-3√3/2 , 3/2)
30 degrees above negative y axis
y = 3 sin 30 = 1.5
x = - 3 cos 30 = -3 (sqrt 3)/2
( -1.5 sqrt 3 , + 1.5 )
that box you always included what does it mean@reiny it confusing me
It is a square root sign I suspect and it is not showing up in your font. Her answer is the same as mine.
yes thanks!!!
To find the Cartesian coordinates of a point given in polar coordinates (r, θ), you can use the following formulas:
x = r * cos(θ)
y = r * sin(θ)
In this case, the polar coordinates of the point are (3, 150 degrees). Let's substitute the values into the formulas to get the Cartesian coordinates:
x = 3 * cos(150°)
y = 3 * sin(150°)
To perform these calculations, we need to convert the angle from degrees to radians, since trigonometric functions in most programming languages expect angles in radians. The conversion formula is:
radians = degrees * π / 180
Converting 150 degrees to radians:
θ (in radians) = 150° * π / 180 ≈ 2.61799388 radians
Now we substitute this value into the Cartesian coordinate formulas:
x ≈ 3 * cos(2.61799388)
y ≈ 3 * sin(2.61799388)
Evaluating these expressions will give us the Cartesian coordinates of the point.