University:
York University
Course:
MATH 1013 | Applied Calculus
Academic year:

2023
Views:

103

Pages:

2
Author:

Niklas

III. Basic TrigonometryUNIT CIRCLE (Ch.4) I. UNIT CIRCLE: unit circle - a circle centered at the origin with a radius of 1. the unit circle is defined by the following parametric equation. x = cosθ y = sinθ (0,1) (cosθ, sinθ) (1,0) (0,0) X (0,-1) II. QUADRANTAL COORDINATES: 0°/0 (1,0) cos0 = 1 ^ sin0 = 0 90°/π/2 (0,1) cosπ/2 = 0 ^ sinπ/2 = 1 180°/π (-1,0) cosπ = -1 ^ sinπ = 0 270°/3π/2 (0,-1) cos3π/2 = 0 ^ sin3π/2 = -1 III. CREATION OF THE UNIT CIRCLE: major values on the unit circle are determined by special right triangles. recall cos60° = sin30° = 1/2 sin60° = cos30° = √3/2 cos45° = sin45° = √2/2 √3/2 √3 60 √2 45 ( 12. (-1,0) 180 IV. THE UNIT CIRCLE: 120 31 135 3 150 (-) 2 210 225 240 5 2 3 270 ↑(0,1) 290 3π 2 (0,-1) 300 V. Evaluating Trigonometric Functions Without A Calculator 60 7 22 () 30 () 0/2π (10) 0360 () (주) sine y = 1. sin 60 3 2 2. tan 1800 3. sin 210 4. tan 135 -1 tan csc04 sec cote 5. cos.sec 2 213 3 2