Angle θ45° (π/4)
Quick Standard Angles
Speed:
ASTC Quadrant Sign Rules
All-Silver-Tea-CupsQuadrant I (0° – 90°)Active
sin +
cos +
tan +
Quadrant II (90° – 180°)
sin +
cos -
tan -
Quadrant III (180° – 270°)
sin -
cos -
tan +
Quadrant IV (270° – 360°)
sin -
cos +
tan -
Active Angle Insight:
At θ = 45°, the horizontal coordinate is x = +0.71 and the vertical coordinate is y = +0.71. A: All trig functions are positive (x > 0, y > 0).
θ = 45° (π/4)cos θ = √2/2sin θ = √2/2tan θ = 1
Connected Wave Projection: Sine Curve y = sin(θ)
The Connected Nature of Mathematics
From Constructions to Functions & Waves
Mathematics links geometric shapes, algebraic equations, and circular periodic motion. In this lab, observe how geometric right triangles give rise to the unit circle coordinates (cos θ, sin θ), which unroll continuously to generate trigonometric wave functions.