Special Right Triangles and Quadrantal Triangles

First and foremost, I want to acknowledge John Paul Aguilar for choosing me to do the next blog.

Special Right Triangles

To determine the exact values of trigonometric ratios, we should first memorize the trigonometric functions and their second functions.

sinθ = Opposite                                  cscθ = Hypotenuse
        Hypotenuse                                           Opposite


cosθ = Adjacent                                 secθ = Hypotenuse
         Hypotenuse                                          Adjacent



tanθ = Opposite                                  cotθ = Adjacent

          Adjacent                                             Opposite



* The special angles on the unit circle are based on reference angles of either 30°, 45° or 60°.

** 30° is the same as π/6
45° is the same as π/4
60° is the same as π/3
90° is the same as π/2
π = 180°


45°, 45°, 90° Triangle





30°, 60°, 90° Triangle with a 30° reference angle




30°, 60°, 90° Triangle with a 60° reference angle




To get the exact value of the trigonometric ratios, just plug in the opposite, hypotenuse or adjacent angles in the SOH CAH TOA.

For example:

1. Determine the exact value of sinθ in the diagram below.



sinθ = Opposite
         Hypotenuse

sinθ = 1/√2


2. Determine the exact value of cotθ in the diagram below.


cotθ = √3




Quadrantal Angles


       The quadrantal angles are shown in degrees and they                                                                   are 0°, 90°, 180° and 270°.


     The quadrantal angles are shown in exact values. They                                                                          are π/2, π, 3π/2 and 2π



Note: Decimals can also be used as labels and they are called approximate values.





FIN

KONIEC


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RAIZZA BONDOC.


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