1.1: Trigonometric Functions
- Page ID
- 143258
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- Express \(\sec(\theta)\), \(\tan(\theta)\), \(\csc(\theta)\), and \(\cot(\theta)\) in terms of \(\sin(\theta)\) and \(\cos(\theta)\).
- Convert \(180^\circ\) from degrees to radians.
- Convert \(\dfrac{\pi}{4}\) from radians to degrees.
- Convert \(270^\circ\) from degrees to radians.
- Convert \(\dfrac{\pi}{6}\) from radians to degrees.
- Convert \(60^\circ\) from degrees to radians.
- Convert \(\dfrac{\pi}{2}\) from radians to degrees.
- Given the triangle below, find two sets of values for the lengths of the sides \(a\), \(b\), and \(c\).
- Given the triangle below, find two sets of values for the lengths of the sides \(a\), \(b\), and \(c\).
- Given the triangle below, find two sets of values for the lengths of the sides \(a\), \(b\), and \(c\).
- Given the triangle below, find \(\sin(\theta)\), \(\cos(\theta)\), \(\sec(\theta)\), \(\tan(\theta)\), \(\csc(\theta)\), and \(\cot(\theta)\).
- Find the reference angle to \(\dfrac{\pi}{3}\).
- Find the reference angle to \(\dfrac{7\pi}{6}\).
- Find the reference angle to \(\dfrac{3\pi}{4}\).
- Find the reference angle to \(\dfrac{11\pi}{6}\).
- Find the reference angle to \(\dfrac{5\pi}{4}\).
- Find the reference angle to \(\dfrac{2\pi}{3}\).
- Find the reference angle to \(\dfrac{9\pi}{4}\).
- Find the reference angle to \(-\dfrac{2\pi}{3}\).
- For what values of \(\theta \in [0, 2\pi]\) is \(\sin \theta = 0\)? For what values of \(\theta \in [0, 2\pi]\) is \(\sin \theta > 0\)? For what values of \(\theta \in [0, 2\pi]\) is \(\sin \theta < 0\)?
- For what values of \(\theta \in [0, 2\pi]\) is \(\cos \theta = 0\)? For what values of \(\theta \in [0, 2\pi]\) is \(\cos \theta > 0\)? For what values of \(\theta \in [0, 2\pi]\) is \(\cos \theta < 0\)?
- For what values of \(\theta \in [0, 2\pi]\) is \(\tan \theta = 0\)? For what values of \(\theta \in [0, 2\pi]\) is \(\tan \theta > 0\)? For what values of \(\theta \in [0, 2\pi]\) is \(\tan \theta < 0\)?
- Given \(\theta = 0\), find \(\sin(\theta)\), \(\cos(\theta)\), \(\sec(\theta)\), \(\tan(\theta)\), \(\csc(\theta)\), and \(\cot(\theta)\).
- Given \(\theta = \dfrac{\pi}{3}\), find \(\sin(\theta)\), \(\cos(\theta)\), \(\sec(\theta)\), \(\tan(\theta)\), \(\csc(\theta)\), and \(\cot(\theta)\).
- Given \(\theta = \dfrac{3\pi}{4}\), find \(\sin(\theta)\), \(\cos(\theta)\), \(\sec(\theta)\), \(\tan(\theta)\), \(\csc(\theta)\), and \(\cot(\theta)\).
- Given \(\theta = \dfrac{\pi}{2}\), find \(\sin(\theta)\), \(\cos(\theta)\), \(\sec(\theta)\), \(\tan(\theta)\), \(\csc(\theta)\), and \(\cot(\theta)\).
- Given \(\theta = 2\pi\), find \(\sin(\theta)\), \(\cos(\theta)\), \(\sec(\theta)\), \(\tan(\theta)\), \(\csc(\theta)\), and \(\cot(\theta)\).
- Given \(\theta = \dfrac{7\pi}{6}\), find \(\sin(\theta)\), \(\cos(\theta)\), \(\sec(\theta)\), \(\tan(\theta)\), \(\csc(\theta)\), and \(\cot(\theta)\).
- Given \(\theta = \dfrac{4\pi}{3}\), find \(\sin(\theta)\), \(\cos(\theta)\), \(\sec(\theta)\), \(\tan(\theta)\), \(\csc(\theta)\), and \(\cot(\theta)\).
- Given \(\theta = \dfrac{3\pi}{2}\), find \(\sin(\theta)\), \(\cos(\theta)\), \(\sec(\theta)\), \(\tan(\theta)\), \(\csc(\theta)\), and \(\cot(\theta)\).
- Given \(\theta = \dfrac{5\pi}{3}\), find \(\sin(\theta)\), \(\cos(\theta)\), \(\sec(\theta)\), \(\tan(\theta)\), \(\csc(\theta)\), and \(\cot(\theta)\).
- Given \(\theta = \pi\), find \(\sin(\theta)\), \(\cos(\theta)\), \(\sec(\theta)\), \(\tan(\theta)\), \(\csc(\theta)\), and \(\cot(\theta)\).
- Given \(\theta = \dfrac{8\pi}{3}\), find \(\sin(\theta)\), \(\cos(\theta)\), \(\sec(\theta)\), \(\tan(\theta)\), \(\csc(\theta)\), and \(\cot(\theta)\).
- Given \(\theta = \dfrac{5\pi}{2}\), find \(\sin(\theta)\), \(\cos(\theta)\), \(\sec(\theta)\), \(\tan(\theta)\), \(\csc(\theta)\), and \(\cot(\theta)\).
- Given \(\theta = -\dfrac{\pi}{4}\), find \(\sin(\theta)\), \(\cos(\theta)\), \(\sec(\theta)\), \(\tan(\theta)\), \(\csc(\theta)\), and \(\cot(\theta)\).
- Given \(\theta = -\pi\), find \(\sin(\theta)\), \(\cos(\theta)\), \(\sec(\theta)\), \(\tan(\theta)\), \(\csc(\theta)\), and \(\cot(\theta)\).
- Given \(\theta = -\dfrac{\pi}{2}\), find \(\sin(\theta)\), \(\cos(\theta)\), \(\sec(\theta)\), \(\tan(\theta)\), \(\csc(\theta)\), and \(\cot(\theta)\).
- Given \(\theta = -\dfrac{8\pi}{3}\), find \(\sin(\theta)\), \(\cos(\theta)\), \(\sec(\theta)\), \(\tan(\theta)\), \(\csc(\theta)\), and \(\cot(\theta)\).
- Find all values of \(\alpha \in [0, 2\pi)\) where \(\sin(\alpha) = \dfrac{1}{\sqrt{2}}\).
- Find all values of \(\alpha \in [0, 2\pi)\) where \(\cos(\alpha) = 0\).
- Find all values of \(\alpha \in [0, 2\pi)\) where \(\tan(\alpha) = -\sqrt{3}\).
- Find all values of \(\alpha \in [0, 2\pi)\) where \(\sec(\alpha) = -2\).
- Find all values of \(\alpha \in [0, 2\pi)\) where \(\cot(\alpha) = -1\).
- Find all values of \(\alpha \in [0, 2\pi)\) where \(\csc(\alpha)\) is undefined.