An Introduction to Triangle Trigonometry

Okay, here we are, basic triangle trigonometry.  Here are a few things that will come in handy:

Trigonometric Properties:

SOH CAH TOA 

sine=((opposite)/(hypotenuse))

cosine=((adjacent)/(hypotenuse))

tangent=((opposite)/(adjacent))

And the less commonly used: CHO SHA CAO

cosecant=((hypotenuse)/(opposite))

secant=((hypotenuse)/(adjacent))

cotangent=((adjacent)/(opposite))

~ Use the functions above when solving for a side

~ Use the inverses of the functions above when solving for an angle.

Naming Parts of a Triangle:

A triangle’s sides are labeled as lowercase letters.

A triangle’s edges are labeled as either capital or greek letters (alpha, beta, gamma, delta, phi, psy, omega, theta, etc).

Geometric Properties:

The sum of the angles of a triangle add up to 180°. In other words, if you know 2 angles of a triangle you can subtract those from 180 to find the third angle!

The sum of the angles of any polygon with 4 or more sides add up to 360°.

Hope this helps!

Oh! I get it now... (The Reflections of a Confused Adv. Math Student)

Yeah, so this is my 1st "blag" posting:

Ok, My first week of advanced math was rather confusing. I know that most of this was taught in Algebra, but honestly, my brain still feels a little rusty after several months without math class. I also happen to be horrible at memorizing steps and formulas, so I hope that with a little bit of extra studying before a test, i'll score decently.

Also, while I'm here ranting about our first week, I want to thank Amy for her explanation on completing the square. I thought I was doing it properly, but I kept on forgetting this part:

Take half of the coefficient on the x-term (divide it by two, and keeping the sign), and then square it. Add the squared value to both sides of the equation:

So, here's what you're really here for, what I get and what I don't.

• I understand these concepts: Distance Formula, Midpoint Formula, Imaginary numbers chart (i need to memorize it though), completing the square (thanks to Amy), quadratic formula (i know how to use it, I just don't have it memorized after all these years), standard form, point form

• I kinda understand these concepts: Synthetic Division, Polynomials, Factoring, slope-intercept form.

• And then, there's parabolas. I absolutely don't get these: they are my mortal enemies, they keep me up at night, and the horrible thing is, they're the only conic section I learned about in my Non-Honors Algebra II class. The rest of the conic sections look even scarier.

So, since I'll be of no help in my attempts at explaining parabolas, and I don't want to explain something that someone else reflected on, I'll be expaining the midpoint formula.

First, you'll need 2 coordinates: like (2,4) & (1,3)

Define the x & y coordinates as: (x1,y1) (x2,y2)

Therefore:

x1=2

y1=4

x2=1

y2=3

now, add your x-values together, and divide the sum of your x-values by 2. This is the final x-value of your midpoint.

add your y-values together, and divide the sum of your y-values by 2. This is the final y-value of your midpoint.

If you did everything correctly, the midpoint of (2,4) & (1,3) should have come out to:

(1.5, 3.5)

Don't panic if you get a half in your answer, as midpoints can be halves.

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So that about wraps up my blog, but before I go, I would like to be added to the pool of people who would like help on *cringes* parabolas. Could we have a review on them Monday?