Trigonometry Formula Sheet
Special Triangles
Trigonometric Graph: Sine & Cosine Function
𝑓(𝑥) = 𝑎 𝑠𝑖𝑛 𝑘(𝑥 − 𝑝) + 𝑞
𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 = 𝑎
𝑝𝑒𝑟𝑖𝑜𝑑 =
𝑎 =
𝑓(𝑥) = 𝑎 𝑐𝑜𝑠 𝑘(𝑥 − 𝑝) + 𝑞
𝑚𝑎𝑥 − 𝑚𝑖𝑛
2
360
𝑘
𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑠ℎ𝑖𝑓𝑡 = 𝑞
𝑞 =
𝑚𝑎𝑥 + 𝑚𝑖𝑛
2
ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑠ℎ𝑖𝑓𝑡 = 𝑝
The easiest way to determine horizontal shift is to determine by how many units the "starting point" (0,0) of y = sin(x) or
(0,1) of y = cos(x), has moved to the right or left.