This chart is very easy to figure out. So remember, SohCahToa. *Sin, is opposite over hypotenuse. So for the first box, is 30 degrees and for sin it would be 1/2. I know this because, for the 30-60-90 triangle, the theta is on 30 degrees, so that means x is the opposite and adjacent is x square root of 3. and Hypotenuse will always be the side right across the 90 degree angle. *Cos, is adjacent over hypotenuse. So for the second box, lets do 45 degrees. For the 45-45-90 triangle, the theta is on 45 degrees. (For 45-45-90 triangle, it doesnt matter where the theta is, the answer will come out the same whichever 45 degrees you use.) Lets say we use the 45 degrees on the right corner, so that 45 deg is theta. That means the opposite is x and adjacent is x also, and hypotenuse will always be across the 90 deg angle, x square root of 2. So the answer is x over x. (adjacent/hypotenuse) *Tan, is opposite over adjacent. So for the third box, we only have 60 degrees left to do, so lets go with that. For the 30-60-90 triangle, the theta is going on be on the 60 degree angle so, the opposite is x square root of 3 and the adjacent is x and ofcourse, how we determine the adjacent side is because we know that the HYPOTENUSE is always ACROSS THE 90 degree angle! (<--and yes i know, i have stated this multiple TIMES..very imp!!) So the hypotenuse is 2x, in this case. Therefore, tan is opposite/adjacent, so x square root of 3 over x...which is simplified into square root of 3. (Because the x's cross out...NO. they DIVIDE out to 1. so..) The answer is square root of 3.
The rest of them (CSC, SEC, and COT) are just opposites of the sin/cos/tan.
This chart is very easy to figure out. So remember, SohCahToa.
ReplyDelete*Sin, is opposite over hypotenuse. So for the first box, is 30 degrees and for sin it would be 1/2. I know this because, for the 30-60-90 triangle, the theta is on 30 degrees, so that means x is the opposite and adjacent is x square root of 3. and Hypotenuse will always be the side right across the 90 degree angle.
*Cos, is adjacent over hypotenuse. So for the second box, lets do 45 degrees. For the 45-45-90 triangle, the theta is on 45 degrees. (For 45-45-90 triangle, it doesnt matter where the theta is, the answer will come out the same whichever 45 degrees you use.) Lets say we use the 45 degrees on the right corner, so that 45 deg is theta. That means the opposite is x and adjacent is x also, and hypotenuse will always be across the 90 deg angle, x square root of 2. So the answer is x over x. (adjacent/hypotenuse)
*Tan, is opposite over adjacent. So for the third box, we only have 60 degrees left to do, so lets go with that. For the 30-60-90 triangle, the theta is going on be on the 60 degree angle so, the opposite is x square root of 3 and the adjacent is x and ofcourse, how we determine the adjacent side is because we know that the HYPOTENUSE is always ACROSS THE 90 degree angle! (<--and yes i know, i have stated this multiple TIMES..very imp!!) So the hypotenuse is 2x, in this case. Therefore, tan is opposite/adjacent, so x square root of 3 over x...which is simplified into square root of 3. (Because the x's cross out...NO. they DIVIDE out to 1. so..) The answer is square root of 3.
The rest of them (CSC, SEC, and COT) are just opposites of the sin/cos/tan.