Chapter 2 - Acute Angles and Right Triangles - Section 2.1 Trigonometric Functions of Acute Angles - 2.1 Exercises: 11

c = 13 $\sin$$B = \frac{12}{13} \cos$$B$ = $\frac{5}{13}$ $\tan$$B = \frac{12}{5} \csc$$B$ = $\frac{13}{12}$ $\sec$$B = \frac{13}{5} \cot$$B$ = $\frac{5}{12}$

Work Step by Step

Pythagorean Theorem: c$^{2}$ = a$^{2}$ + b$^{2}$ a = 5 b = 12 Therefore: c$^{2}$ = 5$^{2}$ + 12$^{2}$ c$^{2}$ = 25 + 144 c$^{2}$ = 169 c = $\sqrt 169$ c = 13 $\sin$$B = \frac{opposite}{hypotenuse} = \frac{b}{c} = \frac{12}{13} \cos$$B$ = $\frac{adjacent}{hypotenuse}$ = $\frac{a}{c}$ = $\frac{5}{13}$ $\tan$$B = \frac{opposite}{adjacent} = \frac{b}{a} = \frac{12}{5} \csc$$B$ = $\frac{hypotenuse}{opposite}$ = $\frac{c}{b}$ = $\frac{13}{12}$ $\sec$$B = \frac{hypotenuse}{adjacent} = \frac{c}{a} = \frac{13}{5} \cot$$B$ = $\frac{adjacent}{opposite}$ = $\frac{a}{b}$ = $\frac{5}{12}$

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