Trigonometric Identities Practice

The Pythagorean Identity states that $$\tan^2x + 1 = \frac{1}{\text{cos}^2x}$$ or equivalently, $$\text{sin}^2x + \text{cos}^2x = 1$$ .

Cotangent is defined as the ratio of the adjacent side to the opposite side in a right triangle, or mathematically, $$\text{cot}x = \frac{\text{cos}x}{\text{sin}x}$$ .

Secant is defined as the reciprocal of cosine, or mathematically, $$\text{sec}x = \frac{1}{\text{cos}x}$$ .

Cosecant is the reciprocal of sine, or mathematically, $$\text{csc}x = \frac{1}{\text{sin}x}$$ .

The simplified expression is $$\text{csc}^2x + \tan^2x$$ .

The simplified expression is $$\frac{\text{sin}x \text{cos}^2x}{\text{sec}x}$$ .

$$\text{csc}\theta = \frac{5}{4}$$ .

A common first strategy is to use a Pythagorean Identity.

Tangent is defined as the ratio of the opposite side to the adjacent side in a right triangle, or mathematically, $$\text{tan}x = \frac{\text{sin}x}{\text{cos}x}$$ .

In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the hypotenuse, and cosine is the ratio of the length of the adjacent side to the hypotenuse.