Trigonometry Finding Angles Coterminal Angles Reference Angles ... - Free Printable

Let’s solve each problem step by step.

We are asked to draw angles in standard position. That means:
- The vertex is at the origin (0,0).
- The initial side lies along the positive x-axis.
- We rotate from the initial side to get the terminal side.
- Positive angles → counterclockwise rotation.
- Negative angles → clockwise rotation.

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Problem 7: Draw -470° in standard position

Step 1: Since this angle is more than 360° in magnitude, we can find a coterminal angle between 0° and 360° by adding or subtracting 360°.

-470° + 360° = -110°
Still negative? Add another 360°:
-110° + 360° = 250°

So, -470° is coterminal with 250° — meaning they end up pointing in the same direction.

Step 2: Where is 250°?
- 180° is straight left (negative x-axis)
- 250° - 180° = 70° past that → so it’s in Quadrant III, 70° below the negative x-axis.

But since the original angle was negative (-470°), we actually rotated clockwise:
- First full circle clockwise: -360° → back to start
- Then another -110° → which lands us at the same place as 250° counterclockwise.

✔ So for drawing: Start on positive x-axis, rotate clockwise 470° total → ends up in Quadrant III, same as 250°.

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Problem 8: Draw 330° in standard position

Step 1: 330° is less than 360°, so no need to adjust.

Step 2: Where is 330°?
- 270° is straight down (negative y-axis)
- 330° - 270° = 60° → so it’s 60° past 270°, going toward the positive x-axis.
→ That puts it in Quadrant IV, 30° above the positive x-axis (since 360° - 330° = 30°).

✔ So for drawing: Start on positive x-axis, rotate counterclockwise 330° → ends up in Quadrant IV, close to the positive x-axis but slightly below it.

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Final Answer:

For problem 7 (-470°): Draw an angle starting from the positive x-axis, rotating clockwise 470° (which is one full circle plus 110° more), ending in Quadrant III, 70° below the negative x-axis.

For problem 8 (330°): Draw an angle starting from the positive x-axis, rotating counterclockwise 330°, ending in Quadrant IV, 30° below the positive x-axis.