Question

Convert polar equation to the standard form of each rectangular equation: θ=-135

Answer 1

`\\ \rm\Rrightarrow \theta=-135`

`\\ \rm\Rrightarrow tan\theta=tan(-135)`

`\\ \rm\Rrightarrow (Perpendicular)/(Base)=tan(-(3\pi)/(4))`

• Perpendicular is y and base is x

`\\ \rm\Rrightarrow (y)/(x)=1`

`\\ \rm\Rrightarrow y=x`

• Convert to standard form Ax+By+C=0

`\\ \rm\Rrightarrow x-y=0`

Answer 2

x - y = 0 is the standard form of the polar equation θ = -135

`\sf \theta \ =-135`

• we should know tan(-135) is 1

`\rightarrow \sf tan(\theta) \ =tan(-135)`

`\rightarrow \sf tan(\theta) \ =1`

`\rightarrow \sf (y)/(x) \ = 1`

`\rightarrow \sf y =x`

`\rightarrow \sf x -y = 0`