Trigonometric Ratios - Practice Questions & MCQ

Trigonometric Functions of Acute Angles

We can define the trigonometric functions in terms of an angle t and the lengths of the sides of the triangle. The adjacent side (=x) is the side closest to the angle (Adjacent means “next to.”). The opposite side (=y) is the side across from the angle. The hypotenuse (=1) is the side of the triangle opposite the right angle.

Sine $\sin \mathrm{t}=\frac{\text{ opposite }}{\text{ hypotenuse }}$
Cosine $\cos \mathrm{t}=\frac{\text{ adjacent }}{\text{ hypotenuse }}$
Tangent $\tan t=\frac{\text{ opposite }}{\text{ adjacent }}$

Reciprocal Functions: In addition to sine, cosine, and tangent, there are three more functions. These too are defined in terms of the sides of the triangle.

$\begin{array}{rl}& \text{ Cosecant }\csc t=\frac{\text{ hypotenuse }}{\text{ opposite }}=\frac{1}{\sin t}\\ & \text{ Secent }\sec t=\frac{\text{ hypotenuse }}{\text{ adjacent }}=\frac{1}{\cos t}\\ & \text{ Cotangent }\cot t=\frac{\text{ adjacent }}{\text{ opposite }}=\frac{1}{\tan t}\end{array}$

Since, the hypotenuse is the greatest side in a right-angle triangle, and  can never be greater than unity and $\text{cosect}$ and $\text{sect}$ can never be less than unity. 

$\text{ Trigonometric Ratios of some Special Angles }$