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 $\quad \cos \mathrm{t}=\frac{\text { adjacent }}{\text { hypotenuse }}$
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.

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

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. 

Trigonometric Ratios of some Special Angles