Chapter 8.4, Problem 63HP

To determine

To explain:

The values of sine and cosine for an acute angle be always less than $1$

Answer to Problem 63HP

The hypotenuse is the longest side of the right angle triangle; the denominator will be always greater than the numerator.

Explanation of Solution

Given information:

The values of sine and cosine for the acute angles of a right triangle were less than $1$ .

Sin is the ratio of opposite side to hypotenuse.

  $Sin=\frac{A}{C}$

Where,

  $A$ : Opposite Side

  $C$ : Hypotenuse

Cosine is the ratio of adjacent side to hypotenuse.

  $Sin=\frac{B}{C}$

Where,

  $B$ : Adjacent Side

  $C$ : Hypotenuse

Since, the hypotenuse is the longest side of the right angle triangle; the denominator will be always greater than the numerator. This will result is answer less than.