6.2 Trigonometric Functions: Unit Circle Approach: Difference between revisions

Latest revision as of 17:37, 26 August 2022

1. The six Trigonometric Functions (general)

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

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

@@ Line 5: / Line 5: @@
 == Lecture notes ==
-:1. The Six Trigonometric Functions <math></math><br>
+:1. The six Trigonometric Functions (general) <math></math><br>
-<math>
+:<math>
 \begin{align}
 \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{align}
+</math>
-\cos{(\theta)} &= \frac{x}{r} & \sec{(\theta)} &= \frac{r}{x}\\[2ex]
+<br>
+:2. The six Trigonometric Functions (unit circle) <math>r=1</math><br>
+:<math>
+\begin{align}
+\sin{(\theta)} &= y & \csc{(\theta)} &= \frac{1}{y}\\[2ex]
+\cos{(\theta)} &= x & \sec{(\theta)} &= \frac{1}{x}\\[2ex]
 \tan{(\theta)} &= \frac{y}{x} & \cot{(\theta)} &= \frac{x}{y} \\[2ex]
 \end{align}