Chapter 8.6, Problem 15CE

a.

To determine

To write: Why sine of an acute angle is always less than one.

Explanation of Solution

Sine of any angle $=\frac{sideoppositetoangle}{hypotenuse}$

As hypotenuse is the longest side,

  $sideoppositetoangle<hypotenuse$

  $\frac{sideoppositetoangle}{hypotenuse}<1$

So,

Sine of any angle $<1$

Hence,

The value of sine of an acute angle is always less than one.

b.

To determine

To write: Why cosine of an acute angle is always less than one.

Explanation of Solution

Cosine of the angle $=\frac{sideadjacenttoangle}{hypotenuse}$

As hypotenuse is the longest side,

  $sideadjacenttoangle<hypotenuse$

  $\frac{sideadjacenttoangle}{hypotenuse}<1$

So,

Cosine of any angle $<1$

Hence,

Cosine of an acute angle is always less than one