M117
Sine over Cosine
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Definition:
Sine, Cosine and Tangent are the main functions used in Trigonometry and are based on a Right-Angled Triangle.
Before getting stuck into the functions, it helps to give a name to each side of a right triangle
"Opposite" is opposite to the angle θ
"Adjacent" is adjacent (next to) to the angle θ
"Hypotenuse" is the long one
HOW TO:
Soh...
Sine = Opposite / Hypotenuse
cah...
Cosine = Adjacent / Hypotenuse
toa
Tangent = Opposite / Adjacent
Khan Link:
https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-trig-ratios-intro/v/basic-trigonometry
Lyrics
Sine over Cosine
I think I’m on a tangent, sine over cosine (repeat 8x)
When a triangle is right the hypotenuse is the side opposite the 90 degree angle
The other angle yet to be defined the side closes to its adjacent
The other is opposite of what we are trying to find
The signs when you divide the hypotenuse by the opposite that gives you rise on a graph
Cosign is so much alike x on a graph it’s just dividing using different sides
Hypotenuse by adjacent finds it every time
Two evaluate the tangent sine over cosine
If the adjacent is 12 and the opposite is 9
Then that means that the tangent is .75
I think I’m on a tangent, sine over cosine (repeat 8x)
Soh, Cah, Toa (repeat 3x)
Let me explain these three trick functions can drive you insane
So what is soh? Well S stands for Sine
Which is opposite over hypotenuse, Soh in a line
Cah is cosine, adjacent over hypotenuse or Cah you see where acronyms have gotten you.
Finally Toah, T stands for tangent
But now we got to dig a little deeper, here we go !
Sine over cosign that’s opposite over hypotenuse divided by adjacent over hypotenuse but realize
According to math principles you can multiply by the reciprocal
That makes it a little easier to handle
Cause both H’s divide out or cancel
So after sticking to the basics we discovered that the tangents opposite over adjacent
These are the three trigonometry functions now you can use them alone or in conjunction
Sine over cosign, I think I’m on a tangent (repeat 3x)
Standards
- CCSS.MATH.CONTENT.HSF.TF.C.9 — (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.