Exercise 26 Page 574

Let's begin with drawing a 45^(∘)-45^(∘)-90^(∘) triangle. If we call the legs of this right isosceles triangle x, then the hypotenuse is xsqrt(2).

In our exercise we are asked to evaluate the tangent of 45^(∘). Recall that the tangent of ∠ A is the ratio of the length of the leg opposite ∠ A to the length of the leg adjacent ∠ A. Using this definition, we can write the appropriate ratio for 45^(∘).

tan 45^(∘)=x/x

ReduceFrac

a/b=.a /x./.b /x.

tan 45^(∘)=1/1

DivByOne

a/1=a

tan 45^(∘)=1

The tangent of 45^(∘) is 1.