Trig Values
📌 Essential Trig Values (Unit Circle)
Q: What is sin(π6)\sin\left(\frac{\pi}{6}\right)sin(6π)?
A: 12\tfrac{1}{2}21
Q: What is cos(π6)\cos\left(\frac{\pi}{6}\right)cos(6π)?
A: 32\tfrac{\sqrt{3}}{2}23
Q: What is tan(π6)\tan\left(\frac{\pi}{6}\right)tan(6π)?
A: 13\tfrac{1}{\sqrt{3}}31 or 33\tfrac{\sqrt{3}}{3}33
Q: What is sin(π4)\sin\left(\frac{\pi}{4}\right)sin(4π)?
A: 22\tfrac{\sqrt{2}}{2}22
Q: What is cos(π4)\cos\left(\frac{\pi}{4}\right)cos(4π)?
A: 22\tfrac{\sqrt{2}}{2}22
Q: What is tan(π4)\tan\left(\frac{\pi}{4}\right)tan(4π)?
A: 111
Q: What is sin(π3)\sin\left(\frac{\pi}{3}\right)sin(3π)?
A: 32\tfrac{\sqrt{3}}{2}23
Q: What is cos(π3)\cos\left(\frac{\pi}{3}\right)cos(3π)?
A: 12\tfrac{1}{2}21
Q: What is tan(π3)\tan\left(\frac{\pi}{3}\right)tan(3π)?
A: 3\sqrt{3}3
Q: What are sin(π)\sin(\pi)sin(π), cos(π)\cos(\pi)cos(π), and tan(π)\tan(\pi)tan(π)?
A: 0,−1,00, -1, 00,−1,0
Q: What are sin(π2)\sin\left(\tfrac{\pi}{2}\right)sin(2π), cos(π2)\cos\left(\tfrac{\pi}{2}\right)cos(2π)?
A: 1,01, 01,0
📌 Special Trig Limit Identities
Q: limx→0sinxx=?\lim_{x\to 0} \frac{\sin x}{x} = ?limx→0xsinx=?
A: 111
Q: limx→0tanxx=?\lim_{x\to 0} \frac{\tan x}{x} = ?limx→0xtanx=?
A: 111
Q: limx→01−cosxx=?\lim_{x\to 0} \frac{1 - \cos x}{x} = ?limx→0x1−cosx=?
A: 000
Q: limx→01−cosxx2=?\lim_{x\to 0} \frac{1 - \cos x}{x^2} = ?limx→0x21−cosx=?
A: 12\tfrac{1}{2}21
📌 Other Key Identities Useful in Limits
Q: What is sin2x+cos2x\sin^2 x + \cos^2 xsin2x+cos2x?
A: 111
Q: What is 1+tan2x1 + \tan^2 x1+tan2x?
A: sec2x\sec^2 xsec2x
Q: What is 1+cot2x1 + \cot^2 x1+cot2x?
A: csc2x\csc^2 xcsc2x