Coordinate Definitions of the Trigonometric Ratios.
- \(\displaystyle \cos (\theta) = \dfrac{x}{r}\)
- \(\displaystyle \sin (\theta) = \dfrac{y}{r}\)
- \(\displaystyle \tan (\theta) = \dfrac{y}{x}\)
\(\theta\) | \(~~~~\cos (\theta)~~~~\) | \(~~~~\sin (\theta)~~~~\) | \(180\degree - \theta\) | \(\cos (180\degree - \theta)\) | \(\sin (180\degree - \theta)\) |
\(10 \degree\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) |
\(20 \degree\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) |
\(30 \degree\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) |
\(40 \degree\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) |
\(50 \degree\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) |
\(60 \degree\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) |
\(70 \degree\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) |
\(80 \degree\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) |
\(\theta\) | \(~~~~\cos (\theta)~~~~\) | \(~~~~\sin (\theta)~~~~\) | \(180\degree - \theta\) | \(\cos (180\degree - \theta)\) | \(\sin (180\degree - \theta)\) |
\(10 \degree\) | \(0.9848\) | \(0.1736\) | \(170\degree\) | \(-0.9848\) | \(0.1736\) |
\(20 \degree\) | \(0.9397\) | \(0.3420\) | \(160\degree\) | \(-0.9397\) | \(0.3420\) |
\(30 \degree\) | \(0.8660\) | \(0.5\) | \(150\degree\) | \(0.8660\) | \(-0.5\) |
\(40 \degree\) | \(0.7660\) | \(0.6428\) | \(140\degree\) | \(-0.7660\) | \(0.6428\) |
\(50 \degree\) | \(0.6428\) | \(0.7660\) | \(130\degree\) | \(-0.6428\) | \(0.7660\) |
\(60 \degree\) | \(0.5\) | \(0.8660\) | \(120\degree\) | \(-0.5\) | \(0.8660\) |
\(70 \degree\) | \(0.3420\) | \(0.9397\) | \(110\degree\) | \(-0.9397\) | \(0.3420\) |
\(80 \degree\) | \(0.1736\) | \(0.9848\) | \(100\degree\) | \(-0.9848\) | \(0.1736\) |
\(\theta\) | \(\cos(\theta)\) | \(\sin(\theta)\) | \(\tan(\theta)\) |
\(120\degree\) | \(\dfrac{-1}{2} \) | \(\dfrac{\sqrt{3}}{2}\) | \(-\sqrt{3} \) |
\(150\degree\) | \(\dfrac{-\sqrt{3}}{2} \) | \(\dfrac{1}{2} \) | \(\dfrac{-1}{\sqrt{3}} \) |
\(\theta\) | \(~~~0\degree~~~\) | \(~~~30\degree~~~\) | \(~~~45\degree~~~\) | \(~~~60\degree~~~\) | \(~~~90\degree~~~\) | \(~~~120\degree~~~\) | \(~~~135\degree~~~\) | \(~~~150\degree~~~\) | \(~~~180\degree~~~\) |
\(\cos (\theta)\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) |
\(\sin (\theta)\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) |
\(\tan (\theta)\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) |
\(\theta\) | \(~~~15\degree~~~\) | \(~~~25\degree~~~\) | \(~~~65\degree~~~\) | \(~~~75\degree~~~\) | \(~~~105\degree~~~\) | \(~~~115\degree~~~\) | \(~~~155\degree~~~\) | \(~~~165\degree~~~\) |
\(\cos (\theta)\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) |
\(\sin (\theta)\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) |
\(\tan (\theta)\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) | \(~\) |