Question

Convert to an equation in rectangular coordinates. 4 cos (0) - sin (0) (Express numbers in exact form. Use symbolic notation and fractions where needed.) equation: Explain your reasoning: This ungraded area will provide insight to your instructor. 500 Characters remaining

Answer 1

`y=4x`

Explanation:

In this question, we are asked to find the rectangular equation of the curve defined by the polar expression:

`4\cos(\theta) - \sin(\theta)`

To achieve this, we can use the polar conversion formulas:

`(x)/(r) = \cos(\theta)` ... also written as
`x = r\cdot \cos(\theta)`

`(y)/(r) = \sin(\theta)` ... also written as
`y = r\cdot \sin(\theta)`

First, we need to form an equation by setting the expression equal to 0.

`4\cos(\theta) - \sin(\theta) = 0`

Next, we can substitute for sine and cosine using the above conversion formulas:

`4\cdot (x)/(r) - (y)/(r) = 0`

From here, we can multiply both sides by r to get rid of the fractions.

`4x - y = 0`

Finally, we can add y to both sides to put the equation in slope-intercept form.

`\boxed{y=4x}`