Trigonometric expressions, identities, and equations

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

The Pythagorean identity states that for any angle $$\theta$$ , $$\tan^2\theta + 1 = \frac{1}{\text{cos}^2\theta}$$ .

The reciprocal identity for sine states that $$\text{csc}(\theta) = \frac{1}{\text{sin}(\theta)}$$ .

The reciprocal identity for cosine states that $$\text{sec}(\theta) = \frac{1}{\text{cos}(\theta)}$$ .

The reciprocal identity for tangent states that $$\text{cot}(\theta) = \frac{1}{\text{tan}(\theta)}$$ .

$$\theta = \frac{7\text{π}}{6}, \frac{11\text{π}}{6}$$ .

$$\text{sec}^2 x$$ .

$$\text{cos} \theta$$ .