Trigonometry functions and Right Triangles First of all, think of a trigonometry function as you would any general function. That is, a value goes in and a value comes out. f(x) = ?

The names of the three primary trigonometry functions are: The names of the three primary trigonometry functions are: –Sine –Cosine –tangent These are abbreviated this way: These are abbreviated this way: –sine..... sin –cosine..... cos –tangent..... tan

A value goes in and a value comes out sin (Θ) = ? sin (Θ) = ? cos (Θ) = ? cos (Θ) = ? tan (Θ) = ? tan (Θ) = ? The input value is Θ. This input value usually represents an angle. The input value is Θ. This input value usually represents an angle. Θ What does the output represent? What does the output represent?

What do these have in common? The value for the sin(Θ) is defined as the value that you get when you divide the opposite side by the hypotenuse. This can be written: The value for the sin(Θ) is defined as the value that you get when you divide the opposite side by the hypotenuse. This can be written: –sin(Θ) = opposite / hypotenuse –So the sin of the angle is simply the ratio between the opposite side and the hypotenuse –Since both triangles have the same angle the ratio between the opposite side and the hypotenuse is the same! They have the same angle!!!

The three trig functions are simply the ratios between the sides of a right triangle. The three trig functions are simply the ratios between the sides of a right triangle. sin(Θ) = opposite / hypotenuse sin(Θ) = opposite / hypotenuse cos(Θ) = adjacent / hypotenuse cos(Θ) = adjacent / hypotenuse tan(Θ) = opposite / adjacent tan(Θ) = opposite / adjacent An easy was to remember which function goes with each ratios is: SOH CAH TOA A calculator looks up the ratio for the angle that you enter. A calculator looks up the ratio for the angle that you enter.

example sin(Θ) = opp / hyp = sin(Θ) = opp / hyp = – 4.00 cm / 7.21 cm = – cos (Θ) = adj / hyp cos (Θ) = adj / hyp tan (Θ) = opp / adj tan (Θ) = opp / adj A= Θ = 33.7 Try typing sin(33.7) into your calc. It gives you the ratio.

Try one! Θ= 40 o Θ= 40 o hyp = 5.5cm Θ Find the length of opposite side. Find the length of opposite side. sin(Θ) = opp / hyp sin(Θ) = opp / hyp Find the length of the adjacent side Find the length of the adjacent side Multiple ways to do it. Multiple ways to do it.

What if you know two of the sides but not the angle? 3cm Θ4cm Θ=?