Chapter 4.3, Problem 1E

To determine

To match : The given trigonometric functions with its right triangle definition.

Answer to Problem 1E

(a) $\sin e$ − (iii) $\frac{\text{opp}}{\text{hyp}}$

(b) $\cos \text{ine}$ − (vi) $\frac{\text{adj}}{\text{hyp}}$

(c) $\tan \text{gent}$ − (ii) $\frac{\text{opp}}{\text{adj}}$

(d) cosecant − (v) $\frac{\text{hyp}}{\text{opp}}$

(e) secant− (i) $\frac{\text{hyp}}{\text{adj}}$

(f) cotangent− (iv) $\frac{\text{adj}}{\text{opp}}$

Explanation of Solution

Given information:

(a) $\sin$ (b) $\cos$ (c) $\tan$ (d) $\csc$ (e) $\sec$ (f) $\cot$

(i) $\frac{\text{hyp}}{\text{adj}}$ (ii) $\frac{\text{opp}}{\text{adj}}$ (iii) $\frac{\text{opp}}{\text{hyp}}$ (vi) $\frac{\text{adj}}{\text{hyp}}$ (v) $\frac{\text{hyp}}{\text{opp}}$ (iv) $\frac{\text{adj}}{\text{opp}}$

The right angle triangle as given below in the diagram, the length of hypotenuse, adjacent and opposite are denoted as $\text{hyp}$ , $\text{adj}$ , $\text{opp}$ .

  

Each trigonometric function given in the question has its own trigonometric ratio with respect to the diagram given.