Thomas_Marks

Tangent= Opposite/Adjacent
Opposite = the length of the side opposite θ Adjacent = the length of the side adjacent to θ Hypotenuse = the length of the hypotenuse


 * [[image:trig1.gif caption="Example of a Trigonometric Triangle"]] ||
 * Example of a Trigonometric Triangle ||

- Sine, Cosine, and Tangent can be used when finding side measurements of right triangles. - When x and a side measurement are given, you can determine which formula you will use.

Sample Problems using above triangle: 1. What is the hypotenuse (H) measurement when x = 60° and O = 10in.? 2. What is the adjacent (A) measurement when x = 21° and H = 30ft.? 3. What is the opposite (O) measurement when x= 5° and A= 27cm.?
 * sin(x) = O/H
 * sin(60°) = O/H
 * sin(60°) = 10in./H
 * H x sin(60°) = 10in.
 * H = 10in./sin(60°)
 * H = 11.55in.
 * cos(x) = A/H
 * cos(21°) = A/H
 * cos(21°) = A/30ft.
 * 30ft. x cos(21°) = A
 * A = 28.00ft.
 * tan(x)= O/A
 * tan(5°) = O/A
 * tan(5°) = O/27cm.
 * 27cm. x tan(5°) = O
 * O = 2.36cm.

===**__Special Triangles to Remember__ (These will make SOCAHTOA easier and faster to find) __Fun Ways to Help Remember Sine, Cosine, and__ __Tangent__**===


 * the old Indian Chief: SOCAHTOA
 * oh **h**eck, **a**nother **h**our **o**f **a**lgebra!
 * oscar **h**ad **a** **h**eap **o**f **a**pples

__Sines, Cosines, and Tangents of Special Angles__
sin 30˚ = sin π/6 = ½ sin 45˚ = sin π/4 = √2/2 sin 60˚ = sin π/3 = √3/2

cos 30˚ = cos π/6 = √3/2 cos 45˚ = cos π/4 = √2/2 cos 60˚ = cos π/3 = ½

tan 30˚ = tan π/6 = √3/3 tan 45˚ = tan π/4 = 1 tan 60˚ = tan π/3 = √3


 * __Practice Problems:__**



Find the exact values of the six trigonometric functions for the triangle.**
 * Use above triangle for practice problems.


 * =  ||= sin ||= cos ||= tan ||= csc ||= sec ||= cot ||
 * **1.** A = 0.6, B = 0.8, C = 1 ||=  ||   ||   ||   ||   ||   ||
 * **2.** A = 1, B = 1, C = √2, a = 45°, b = 45° ||  ||   ||   ||   ||   ||   ||
 * **3.** A = √3, B = 1, C = 2 ||  ||   ||   ||   ||   ||   ||
 * **4.** A = 4, B = 3, C = 5 ||  ||   ||   ||   ||   ||   ||
 * **5.** A = 6, B = 3 ||  ||   ||   ||   ||   ||   ||
 * **6.** B = 2, C = 6 ||