Solve dx/dθ=a(1-cosθ)quaddy/dθ

$$\frac { d x } { d \theta } = a ( 1 - \cos \theta ) \quad \frac { d y } { d \theta }$$

Solve for a

$$a\in \mathrm{R}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$a\left(1-\cos(\theta )\right)\frac{\mathrm{d}}{\mathrm{d}\theta }(y)=\frac{\mathrm{d}}{\mathrm{d}\theta }(x)$$

Use the distributive property to multiply a by 1-\cos(\theta ).

$$\left(a-a\cos(\theta )\right)\frac{\mathrm{d}}{\mathrm{d}\theta }(y)=\frac{\mathrm{d}}{\mathrm{d}\theta }(x)$$

Use the distributive property to multiply a-a\cos(\theta ) by \frac{\mathrm{d}}{\mathrm{d}\theta }(y).

$$a\frac{\mathrm{d}}{\mathrm{d}\theta }(y)-a\cos(\theta )\frac{\mathrm{d}}{\mathrm{d}\theta }(y)=\frac{\mathrm{d}}{\mathrm{d}\theta }(x)$$

Combine all terms containing a.

$$\left(\frac{\mathrm{d}}{\mathrm{d}\theta }(y)-\cos(\theta )\frac{\mathrm{d}}{\mathrm{d}\theta }(y)\right)a=\frac{\mathrm{d}}{\mathrm{d}\theta }(x)$$

The equation is in standard form.

$$\text{true}$$

This is true for any a.

$$a\in \mathrm{R}$$

Solve for x

$$x\in \mathrm{R}$$