Question

find the cartesian coordinates of the point whose polar coordinates are ( 3/4 ,135°)​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

( -3√2/8 , 3√2/8) is Cartesian coordinates of the point whose polar coordinates are ( 3/4 ,135°)​

Given:

• Polar coordinate (3/4 , 135°)​

To Find:

• The cartesian coordinates

Solution

• For Polar coordinate (r ,θ ) , cartesian coordinates are given by (rcosθ , rsinθ)
• x = rcosθ , y = rsinθ   ( x , y) is cartesian coordinate

Step 1:

Find x coordinate as x = rcosθ and substitute r = 3/4 and θ = 135°

x = (3/4)cos135°

Step 2:

Use cos135° = -1/√2  and calculate value of x

x = (3/4)(-1/√2)

x = -3√2/8

Step 3:

Find y coordinate as y = rsinθ and substitute r = 3/4 and θ = 135°

y = (3/4)sin135°

Step 4:

Use sin135° =  1/√2  and calculate value of y

y = (3/4) (1/√2)

y =  3√2/8

Hence (x , y)  is ( -3√2/8 , 3√2/8)

( -3√2/8 , 3√2/8) is Cartesian coordinates of the point whose polar coordinates are ( 3/4 ,135°)​