M117

Sine over Cosine

MathematicsGrade 12Grade 11Grade 10Grade 9

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Sine over Cosine

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.