1.1: Trigonometric Functions

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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 $c$.
$A right triangle with an angle equal to pi/6. The side adjacent to this angle is labeled a, the side opposite this angle is labeled b, and the hypothenuse is labeled c.$
Given the triangle below, find two sets of values for the lengths of the sides $a$, $b$, and $c$.
$A right triangle with an angle equal to pi/4. The side adjacent to this angle is labeled a, the side opposite this angle is labeled b, and the hypothenuse is labeled c.$
Given the triangle below, find two sets of values for the lengths of the sides $a$, $b$, and $c$.
$A right triangle with an angle equal to pi/3. The side adjacent to this angle is labeled a, the side opposite this angle is labeled b, and the hypothenuse is labeled c.$
Given the triangle below, find $\sin(\theta)$, $\cos(\theta)$, $\sec(\theta)$, $\tan(\theta)$, $\csc(\theta)$, and $\cot(\theta)$.
$A right triangle with acute angle theta, whete the side adjacent to theta is 2, the side opposite theta is sqrt(5), and the hypotenuse is 3.$
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.

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