Basics of Trigonometry

Basics of Trigonometry

1. sinθ=Opposite SideHypotenuse=ABOB 1. \ \sin \theta = \frac {\text{Opposite Side}}{\text{Hypotenuse}} = \frac {AB}{OB}
2. cosθ=Adjacent SideHypotenuse=OAOB 2. \ \cos \theta = \frac {\text{Adjacent Side}}{\text{Hypotenuse}} = \frac {OA}{OB}
3. tanθ=Opposite SideAdjacent Side=ABOA 3. \ \tan \theta = \frac {\text{Opposite Side}}{\text{Adjacent Side}} = \frac {AB}{OA}
4. secθ=HypotenuseAdjacent Side=OBAB 4. \ \sec \theta = \frac {\text{Hypotenuse}}{\text{Adjacent Side}} = \frac {OB}{AB}
5. cosecθ=HypotenuseOpposite Side=OBOA 5. \ \text{cosec} \theta = \frac {\text{Hypotenuse}}{\text{Opposite Side}} = \frac {OB}{OA}
6. cotθ=Adjacent SideOpposite Side=OAAB 6. \ \cot \theta = \frac {\text{Adjacent Side}}{\text{Opposite Side}} = \frac {OA}{AB}

Example:

Determine the six trigonometric ratios for angle D in the right triangle below.

sinθ=Opposite SideHypotenuse=45 \sin \theta = \frac {\text{Opposite Side}}{\text{Hypotenuse}} = \frac 45
cosθ=Adjacent SideHypotenuse=35 \cos \theta = \frac {\text{Adjacent Side}}{\text{Hypotenuse}} = \frac 35
tanθ=Opposite SideAdjacent Side=43 \tan \theta = \frac {\text{Opposite Side}}{\text{Adjacent Side}} = \frac 43
secθ=HypotenuseAdjacent Side=54 \sec \theta = \frac {\text{Hypotenuse}}{\text{Adjacent Side}} = \frac 54
cosecθ=HypotenuseOpposite Side=53 \text{cosec} \theta = \frac {\text{Hypotenuse}}{\text{Opposite Side}} = \frac 53
cotθ=Adjacent SideOpposite Side=34 \cot \theta = \frac {\text{Adjacent Side}}{\text{Opposite Side}} = \frac 34

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