5.6 Trigonometric graphs, exact values
Sine
Domain: \(x∈ℝ \qquad\) Range: \(-1≤y≤1\)
Periodicity: \(360\degree\) or \(2\pi\)
Cosine
Domain: \(x∈ℝ \qquad\) Range: \(-1≤y≤1\)
Periodicity: \(360\degree\) or \(2\pi\)
Tangent
Domain: \(x∈ℝ, x\neq90\degree \qquad\) Range: \(y∈ℝ\)
Periodicity: \(180\degree\) or \(\pi\)
Asymptote: \(x=90\degree, 270\degree, ...\) or \(x=\dfrac{\pi}{2}, \dfrac{3\pi}{2}, ...\)
Domain: \(x∈ℝ \qquad\) Range: \(-1≤y≤1\)
Periodicity: \(360\degree\) or \(2\pi\)
\(\sin{0\degree}=\sin{0}=0\)
\(\sin{30\degree}=\sin{\dfrac{\pi}{6}}=\dfrac{1}{2}\)
\(\sin{30\degree}=\sin{\dfrac{\pi}{6}}=\dfrac{1}{2}\)
\(\sin{45\degree}=\sin{\dfrac{\pi}{4}}=\dfrac{1}{\sqrt{2}}\)
\(\sin{60\degree}=\sin{\dfrac{\pi}{3}}=\dfrac{\sqrt{3}}{2}\)
\(\sin{60\degree}=\sin{\dfrac{\pi}{3}}=\dfrac{\sqrt{3}}{2}\)
\(\sin{90\degree}=\sin{\dfrac{\pi}{2}}=1\)
\(\sin{180\degree}=\sin{\pi}=0\)
\(\sin{180\degree}=\sin{\pi}=0\)
Cosine
Domain: \(x∈ℝ \qquad\) Range: \(-1≤y≤1\)
Periodicity: \(360\degree\) or \(2\pi\)
\(\cos{0\degree}=\cos{0}=1\)
\(\cos{30\degree}=\cos{\dfrac{\pi}{6}}=\dfrac{\sqrt{3}}{2}\)
\(\cos{30\degree}=\cos{\dfrac{\pi}{6}}=\dfrac{\sqrt{3}}{2}\)
\(\cos{45\degree}=\cos{\dfrac{\pi}{4}}=\dfrac{1}{\sqrt{2}}\)
\(\cos{60\degree}=\cos{\dfrac{\pi}{3}}=\dfrac{1}{2}\)
\(\cos{60\degree}=\cos{\dfrac{\pi}{3}}=\dfrac{1}{2}\)
\(\cos{90\degree}=\cos{\dfrac{\pi}{2}}=0\)
\(\cos{180\degree}=\cos{\pi}=1\)
\(\cos{180\degree}=\cos{\pi}=1\)
Tangent
Domain: \(x∈ℝ, x\neq90\degree \qquad\) Range: \(y∈ℝ\)
Periodicity: \(180\degree\) or \(\pi\)
Asymptote: \(x=90\degree, 270\degree, ...\) or \(x=\dfrac{\pi}{2}, \dfrac{3\pi}{2}, ...\)
\(\tan{0\degree}=\tan{0}=0\)
\(\tan{30\degree}=\tan{\dfrac{\pi}{6}}=\dfrac{1}{\sqrt{3}}\)
\(\tan{30\degree}=\tan{\dfrac{\pi}{6}}=\dfrac{1}{\sqrt{3}}\)
\(\tan{45\degree}=\tan{\dfrac{\pi}{4}}=1\)
\(\tan{60\degree}=\tan{\dfrac{\pi}{3}}=\sqrt{3}\)
\(\tan{60\degree}=\tan{\dfrac{\pi}{3}}=\sqrt{3}\)
\(\tan{90\degree}=\tan{\dfrac{\pi}{2}}=undefined\)
\(\tan{180\degree}=\tan{\pi}=0\)
\(\tan{180\degree}=\tan{\pi}=0\)
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