6.2 Trigonometric Functions: Unit Circle Approach

Lecture

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Lecture notes

1. The six Trigonometric Functions (general) ${\displaystyle }$

${\begin{aligned}\sin {(\theta )}&={\frac {y}{r}}&\csc {(\theta )}&={\frac {r}{y}}\\[2ex]\cos {(\theta )}&={\frac {x}{r}}&\sec {(\theta )}&={\frac {r}{x}}\\[2ex]\tan {(\theta )}&={\frac {y}{x}}&\cot {(\theta )}&={\frac {x}{y}}\\[2ex]\end{aligned}}$

2. The six Trigonometric Functions (unit circle) $r=1$

${\begin{aligned}\sin {(\theta )}&=y&\csc {(\theta )}&={\frac {1}{y}}\\[2ex]\cos {(\theta )}&=y&\sec {(\theta )}&={\frac {1}{x}}\\[2ex]\tan {(\theta )}&={\frac {y}{x}}&\cot {(\theta )}&={\frac {x}{y}}\\[2ex]\end{aligned}}$

Solutions

Mr. V solutions: 14, 32, 48, 78, 98, 112

Block #1

13 14 15 17 19

Block #2

31 32 33 35 37 39 41 43 45

Block #3

47 48 49 51 53 55 57 59 61 63

Block #4

77 78 79 81 83

Block #5

85 87 89 91 93

Block #6

95 97 98 99 101 103 105

Block #7

107 109 111 112 113 115