Trigonometry Problems 1-4

Angle 135°

• Lies in the second quadrant.
• Standard position: Starts from the positive x-axis and rotates counter-clockwise to 135°.
• Reference angle: 180° - 135° = 45°.

Angle 450°

• Equivalent to 90° when reduced to a single rotation (450° - 360°).
• Lies in the first quadrant.
• Standard position: Rotates counter-clockwise to 90°.
• Reference angle: 90° - 90° = 0° (90° itself is the angle).

Angle -2π/3

• Equivalent to +π/3 when added to 2π (positive full rotation).
• Lies in the third quadrant.
• Standard position: Starts from the positive x-axis and rotates clockwise to -2π/3.
• Reference angle: π + 2π/3 = 5π/3; so reference angle = 5π/3 - π = 2π/3.

Angle 11π/4

• Equivalent to 3π/4 when reduced by 2π (11π/4 - 8π/4).
• Lies in the second quadrant.
• Standard position: Rotates counter-clockwise to get to 3π/4.
• Reference angle: 180° - 3π/4 (or π - 3π/4 = π/4).