This week we started our unit of trigonometry. The reason we use trigonometry is when we need to find different sides or angles of a right triangle. What we’re learning right now in trigonometry is basically that it’s split into 3 trig functions: sine, cosine and tangent. I chose three triangles from the book that make us use each function. The steps are basically the same when using each function, it’s choosing which function to use that’s the tricky part.

  1. Sine. In this example we need to find “e” which in respect to the angle that’s 19 degrees, is the opposite. We also have the hypotenuse so now we know we’re using opposite and hypotenuse which codes for SOH. We write down which trig function were doing first, then the degree of the angle in brackets, then O over H, if were using SOH. In this case the equation is: sin(19) = e/8.2. To get “e” on it’s own we multiply both sides by 8.2 to now give us: 8.2 sin(19) = e. We put that in our calculators and we get 2.7 = e.

2. Tangent. In this example we need to find “g” which happens to be the opposite. We also have the measurement for the adjacent, which now we know we have to use “TOA”. We start off the same way we did for #1 by writing “tan” first, then the degree then O over A, so now we have tan (64) = g/1.9. To get “g” on its own we multiply both sides by 1.9 and we end up with: 1.9 tan (64) = g and if we put that in our calculator we get 3.9 = g.

3. Cosine. In this example we need to find “i” which is the adjacent. We have the measurement for the hypotenuse which is 13.5 so we know were using adjacent and hypotenuse which means “CAH”. We begin with writing cos, then the degree, then A over H and so we get cos (66) = i/13.5. Just like we did with the other ones we’re going to get “i” by itself by multiplying each side by 13.5 and getting 13.5 cos(66) = i. If we put this in a calculator we would get 5.5 = i.