Find r in component form if $θ$ is the standard angle.

1. $\| \textbf{r} \|=5$ and $θ = \frac { \pi } { 6 }$

   Hint (a):

   Draw each vector in a circle. Then make a right triangle with the $x$-axis.

   Step 1(a):

   Circle, radius in first quadrant, labeled 5, is hypotenuse in right triangle where horizontal leg is part of x axis, central angle of triangle labeled 1 sixth pi = 30 degrees.

   Step 2(a):

   Solve the rest of the triangle.
   Note: Each part forms a special right triangle.

   Labels added, horizontal leg, 5 halves times square root of 3, vertical leg, 5 halves.

   

   

2. $\| \textbf{r} \|=10$ and $θ = \frac { 5 \pi } { 4 }$

3. $\| \textbf{r} \|=15$ and $θ = \frac { 2 \pi } { 3 }$