Unit Circle (Degrees) Flashcards
sin 0°
y/r = 0/1 = 0
sin 30°
y/r = 1/2 / 1 = 1/2 (show a △ with 30° in standard position, so an equilateral triangle goes across the x-axis)
sin 45°
y/r = √2/2 / 1 = √2/2 (show a △ with 45° in standard position)
sin 60°
y/r = √3/2 / 1 = √3/2 (show a △ with 60° in standard position, with equilateral triangle cut in half)
sin 90°
y/r = 1/1 = 1
sin 120°
y/r = √3/2 / 1 = √3/2 (show the 60° reference △)
sin 135°
y/r = √2/2 / 1 = √2/2 (show the 45° reference △)
sin 150°
y/r = 1/2 / 1 = 1/2 (show the 30° reference △, with the equilateral triangle across the x-axis)
sin 180°
y/r = 0/1 = 0
sin 210°
y/r = -1/2 / 1 = -1/2 (show the 30° reference △, with the equilateral triangle across the x-axis)
sin 225°
y/r = -√2/2 / 1 = -√2/2 (show the 45° reference △)
sin 240°
y/r = -√3/2 / 1 = -√3/2 (show the 60° reference △)
sin 270°
y/r = -1/1 = -1
sin 300°
y/r = -√3/2 / 1 = -√3/2 (show the 60° reference △)
sin 315°
y/r = -√2/2 / 1 = -√2/2 (show the 45° reference △)
sin 330°
y/r = -1/2 / 1 = -1/2 (show the 30° reference △, with the equilateral triangle across the x-axis)
cos 0°
x/r = 1/1 = 1
cos 30°
x/r = √3/2 / 1 = √3/2 (show a △ with 30° in standard position, so an equilateral triangle goes across the x-axis)
cos 45°
x/r = √2/2 / 1 = √2/2 (show a △ with 45° in standard position)
cos 60°
x/r = 1/2 / 1 = 1/2 (show a △ with 60° in standard position, with equilateral triangle cut in half)
cos 90°
x/r = 0/1 = 0
cos 120°
x/r = -1/2 / 1 = -1/2 (show a △ with 60° in standard position, with equilateral triangle cut in half)
cos 135°
x/r = -√2/2 / 1 = -√2/2 (show a △ with 45° in standard position)
cos 150°
x/r = -√3/2 / 1 = -√3/2 (show a △ with 30° in standard position, so an equilateral triangle goes across the x-axis)
cos 180°
x/r = -1/1 = -1
cos 210°
x/r = -√3/2 / 1 = -√3/2 (show a △ with 30° in standard position, so an equilateral triangle goes across the x-axis)
cos 225°
x/r = -√2/2 / 1 = -√2/2 (show a △ with 45° in standard position)
cos 240°
x/r = -1/2 / 1 = -1/2 (show a △ with 60° in standard position, with equilateral triangle cut in half)
cos 270°
x/r = 0/1 = 0
cos 300°
x/r = -1/2 / 1 = -1/2 (show a △ with 60° in standard position, with equilateral triangle cut in half)
cos 315°
x/r = √2/2 / 1 = √2/2 = 1/√2 (show a △ with 45° inside the angle)
cos 330°
x/r = √3/2 / 1 = √3/2 (show a △ with 30° in standard position, so an equilateral triangle goes across the x-axis)
tan 0°
y/x = 0/1 = 0
tan 30°
y/x = 1/2 / √3/2 = 1/√3 (show a △ with 30° in standard position, so an equilateral triangle goes across the x-axis)
tan 45°
y/x = √2/2 / √2/2 = 1 (show a △ with 45° in standard position)
tan 60°
y/x = √3/2 / 1/2 = √3 (show a △ with 60° in standard position, with equilateral triangle cut in half)
tan 90°
1/0, which is undefined
tan 120°
y/x = √3/2 / -1/2 = -√3 (show a △ with 60° in standard position, with equilateral triangle cut in half)
tan 135°
y/x = √2/2 / -√2/2 = -1 (show a △ with 45° in standard position)
tan 150°
y/x = 1/2 / -√3/2 = -1/√3 (show a △ with 30° in standard position, so an equilateral triangle goes across the x-axis)
tan 180°
y/x = 0/1 = 0
tan 210°
y/x = -1/2 / -√3/2 = 1/√3 (show a △ with 30° in standard position, so an equilateral triangle goes across the x-axis)
tan 225°
y/x = -√2/2 / -√2/2 = 1 (show a △ with 45° in standard position)
tan 240°
y/x = -√3/2 / -1/2 = √3 (show a △ with 60° in standard position, with equilateral triangle cut in half)
tan 270°
y/x = -1/0, which is undefined
tan 300°
y/x = -√3/2 / 1/2 = -√3 (show a △ with 60° in standard position, with equilateral triangle cut in half)
tan 315°
y/x = -√2/2 / √2/2 = -1 (show a △ with 45° in standard position)
tan 330°
y/x = -1/2 / √3/2 = -1/√3 (show a △ with 30° in standard position, so an equilateral triangle goes across the x-axis)
