In Exercises 54–60, convert each polar equation to a rectangular ...

Question

In Exercises 54–60, convert each polar equation to a rectangular equation. Then use your knowledge of the rectangular equation to graph the polar equation in a polar coordinate system.

θ = 3π/4

Accepted Answer

Convert the given polar equation to a rectangular equation and plot the polar equation using the knowledge of the rectangular equation where the equals five pi divided by six. And here we have a polar graph to put our line on now to graph this, we need to know the equation for data. Now, I don't have a direct equation for data, but we do know some tangent formulas that we have. For example, we have the 10 of data S equals to Y divided by X. Now we can solve for data by taking the inverse tangent of both sides, add the inverse tangent to get the as equals to 10 and verse of Y divided by X. Now it tells us status equals to five pi divided by six. So we will get five pi divided by six equals and inverse Y divided by X. Now let's get rid of our tan inverse by taking tan on both sides. Again, we get 10 of five pi divided by six which from our unit circle, we know what value this is, this is negative S code of three divided by three. On the right side, we will just end up with Y divided by X. Now our equation will be in terms of Y equals. So let's multiply both sides by X to get rid of the X. On the right side, we hit Y equals negative square of three divided by three multiplied by X. This will be our rectangular equation on the graph. We can plot this line. This line follows from the angle five pi divided by six down 2 11 pi divided by six. OK. I hope to help you solve the problem. Thank you for watching. Good bye.

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In Exercises 54–60, convert each polar equation to a rectangular equation. Then use your knowledge of the rectangular equation to graph the polar equation in a polar coordinate system. θ = 3π/4