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The image contains a question about determining the equation of a tangent line to a curve and graphing it. The vector equation is given as:

\[
\mathbf{r}(t) = \left( \cos t + \cos 2t \right) \mathbf{i} + \left( \sin t + \sin 2t \right) \mathbf{j}
\]

The task is to find the tangent line to the curve at the point (-1, -1), where \(\mathbf{r}(t)\) represents a parametric curve. 

To approach the problem:
1. **Differentiate \(\mathbf{r}(t)\) to find the tangent vector**.
   \[
   \mathbf{r}'(t) = \frac{d}{dt}\left[\cos t + \cos 2t \right]\mathbf{i} + \frac{d}{dt}\left[\sin t + \sin 2t \right]\mathbf{j}
   \]

   \[
   \mathbf{r}'(t) = \left[-\sin t - 2\sin 2t \right]\mathbf{i} + \left[\cos t + 2\cos 2t \right]\mathbf{j}
   \]

2. **Find the value of \(t\) that gives the point (-1, -1)**. This is solved by setting the parametric equations equal to the given coordinates:
   - \(\cos t + \cos 2t = -1\)
   - \(\sin t + \sin 2t = -1\)

   Solving this system will provide the value of \(t\) at which the tangent is to be calculated.

3. **Substitute the value of \(t\) into \(\mathbf{r}'(t)\)** to get the tangent vector at that point.

4. **Write the parametric equation of the tangent line using the point (-1, -1) and the tangent vector found in step 3**.

Would you like to go through the complete step-by-step solution?

Tentukan persamaan garis singgung pada kurva fungsi dan garis singgungnya pada kurva titik yang diberikan (-1,-1).

Determine the equation of the tangent line to the parametric curve r(t) = (cos t + cos 2t) i + (sin t + sin 2t) j at the point (-1, -1). Includes differentiation of parametric equations and tangent vector calculation.

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