# Chapter 2 - Acute Angles and Right Triangles - Section 2.1 Trigonometric Functions of Acute Angles - 2.1 Exercises: 58

cos 45° = 1

#### Work Step by Step

$\cot$ 45$^{\circ}$ We must find side x of the 45$^{\circ}$ - 45$^{\circ}$ Right Triangle. Pythagorean Theorem: c$^{2}$ = a$^{2}$ + b$^{2}$ x$^{2}$ = 1$^{2}$ + 1$^{2}$ x$^{2}$ = 2 x = $\sqrt2$ Now consider the triangle from the perspective of a 45$^{\circ}$ angle. Hypotenuse = $\sqrt2$ Opposite = 1 Adjacent = 1 $\cot$ 45$^{\circ}$ = $\frac{Adjacent}{Opposite}$ = $\frac{1}{1}$ = 1 Therefore: cos 45° = 1

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.