H1.+Identify+and+find+the+value+of+trigonometric+ratios+in+right+triangles

=H1. Identify and find the value of trigonometric ratios in right triangles.=

1. What you need to understand:
Trigonometric ratios in right triangles are based on the relation of two side lengths to a given angle. The expression most commonly used, SOHCAHTOA, demonstrates what trigonometric function to use, however it is also necessary to understand what each letter means. S in sohcahtoa, is sine, more commonly "sin". O in sohcahota, is opposite, the opposite side of the right triangle. H in sohcahtoa, is hypotenuse, the hypotenuse of the right triangle. C in sohcahtoa, is cosine, more commonly "cos". A in sohcahtoa, is adjacent, the adjacent side of the right triangle. T in sohcahtoa, is tangent, more commonly "tan". Now that the letters have a meaning, the order the letters in SOHCAHTOA also have a meaning. Sine is relative to opposite and hypotenuse, because opposite divided by hypotenuse gives you the value of sine for the given angle in the situation. Sin(x) = O/H, x being the given angle. Cosine and Tangent also have similar functions with their corresponding letters. Cos(x) = A/H, or the Cosine of x is the same ratio as adjacent divided by hypotenuse. Tan(x) = O/A, or the Tangent of x is the same ratio as opposite divided by adjacent.

2. Example problem:
To truly understand the above functions, take the below triangle for example. If we say that the value of theta in this particular scenario is 30°, we can calculate the sine, cosine, and tangent of the angle if we have the appropriate side lengths. If the length of the hypotenuse is 5, the adjacent is 4, and the opposite is 3, we can calculate the tangent, cosine, and sine.

For this triangle, if you're computing sine, you will take the opposite and hypotenuse of the triangle, 3 and 5, and divide 3 by 5, to get .6. If you're computing cosine, you will take the adjacent and hypotenuse of the triangle, 4 and 5, and divide 4 by 5, to get .8. If you're computing tangent, you will take the opposite and adjacent of the triangle, 3 and 4, and divide 3 by 4 to get .75.

3. Common mistakes or misunderstandings:
A lot of errors when using trigonometry are centered around basic ideas that students are unsure about. For example, knowing that the opposite and adjacent of a right triangle will change depending on the given position of the angle, following the rules as discussed in 1. What you need to understand, knowing exactly what sides you are working with will dictate what trigonometric function you use, as dictated by sohcahtoa. Depending on what sides you have, as you must have two to compute a trigonometric function, computing values using trigonometry will change.

4. For more information:
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Cited Sources:
· http://www.mathsteacher.com.au/year10/ch15_trigonometry/01_ratios/Image3125.gif · http://algebra2c.wikispaces.com/file/view/TrigTriangle.GIF/33994139/TrigTriangle.GIF