BQ#5 – Unit T Concepts 1-3

Why do sine and cosine not have asymptotes, but the other four trig functions do?

Sine has a ratio of opposite over hypotenuse and cosine has a ratio of adjacent over hypotenuse. In the unit circle the hypotenuse is always going to be one. You can't have any asymptotes because in order to get asymptotes on the graph you would need a zero to be divided and you can't divide by zero if you do zero is undefined. When a trig function is undefined it means it has asymptotes and since sine and cosine are not undefined they do not have asymptotes. 

BQ#2: Unit T: Concept Intro

How do the trig graphs relate to the Unit Circle? 

The period for sine and cosine is 2pi because that's how much the distance is for the pattern of sine and cosine to repeat they have to go a full revolution in the unit circle whereas the period of cotangent and tangent is pi because it only takes a half a revolution for these two to repeat their patterns. 

The unit circle only reaches a radius of one, we all know that, and sine and cosine have one as their amplitude because of the unit circles radius. Other trig functions don't have restrictions which is why they don't have amplitudes

Reflection #1: Unit Q: Concept 1-5

What does it actually mean to verify a trig function?

To verify a trig function is when you have one of the problems like in one of the concepts 1 or 5 and then just equaling the left side to the right side. It is like you are given a puzzle and you have a picture of the puzzle completed but you only have puzzle pieces. You have to put the pieces together to get it to look like the picture. It's as simple as that, but contains more math and is more challenging. 

What tips and tricks have you found helpful? 

Some tips that I recommend are to look at the problem and look for simple things to do or change don't over think the problem because the answer will fly by your head. Some tricks that I use is to actually memorize the identities that way you don't have to keep referring to your SSS packet. 

Explain your thought process and steps you take in verifying a trig identity.

My thought process first is to recognize what I have and look for simple things to do. I always try a few things like looking for a GCF, Substituting an identity, The conjugate, CLT, Separating fractions, and factoring. I try looking to see if any of these will work most of the time the problems are simple, but I overthink everything and do way more than I have to. Then make sure to write the steps that you have taken in order to receive credit, but to also help you remember what you had done in order to get that answer. Personally I think verifying is easier than simplifying because verifying already gives you the answer and when you simplify you are not sure whether you are right or not. 

SP# 7: Unit Q Concept 2: Find all Trig Functions when given one trig function and quadrant (using identities and SOH CAH TOA)

Please see my SP7, made in collaboration with Ivan L, by visiting their blog here.  Also be sure to check out the other awesome posts on their blog

I/D #3 Unit Q: Pythagorean Identities

Inquiry Activity Summary:

1. Where does sinx^2+cosx^2=1 come from?

In earlier units we learned about the three basic trig functions which are sin, cosine, and tangent. Sine which means x/r so the y is the side that rises and r is the hypotenuse. R replaces the c^2 in the Pythagorean theorem. So it would really be a^2+b^2=R^2. Cosine we know is y/r   . We know that when looking at the problem above that it really is x/r^2+y/r^2=1. Using the unit circle to help prove that this statement is true is fairly easy we use the 45-45-90 triangle. Which is square root of 2/2, square root of 2/2. When squaring these you get one half plus one half equals one. Which in this case is an identity which means it is a true proven statement. 

2. Show and explain how to derive the two remaining Pythagorean Identities from sin^2x+cos^2x=1

To derive the two remaining identities all you have to do is divide by either cosine or sine. We know that if we divide by the same function we will get one so that is how we get the one on the right side. We will also notice that if we divide by a trig function like sin/cos we simplify that to x/r /y/r we multiply the reciprocal of the denominator to top and bottom to get the new one which is tangent. You do the  same thing for the other identity. 

Inquiry Reflection Activity 

1. The connection I see between Units N, O, and P are that we still have to use the unit circle in some we and that we still use the trig functions even more. 

2. If I had to describe trigonometry in 3 words, they would be challenging, depressing, frustrating. 

WPP #13 & 14: Unit P Concept 6 & 7 - Applications with Law of Sines and Law of Cosines

Please see my WPP13-14, made in collaboration with Ivan L, by visiting their blog here.  Also be sure to check out the other awesome posts on their blog

BQ#1:Unit P: Concept 1 and 4: Law of Sines and Area Formulas

1. Law of Sines 
We need the law of sines to help determine the missing sides of an oblique triangle. We can also use it to determine the sides of a right triangle. Sin is opposite/ hypotenuse. When we have a problem we will always be given an angle we use one of those angles to help us determine one of the missing sides. The law of sines comes from trig. Sine is only used for right triangles but with non right triangles we can use them too. When we use some we have to make sure the question gives us AAS or ASA 

4. Area Formulas 

Always remember that the area of a right triangle will always be 1/2 bh. B is the base and h is the height. We will not always be given the height so we have to find the height using sine. You use the same method of finding the area of a right triangle for finding the one of an oblique triangle. You split the oblique triangle in half or wherever you can so you can determine the height. Use an angle given to you to determine one of the sides. You keep going until you find the height and use the same equation. It will always relate to the area of a triangle formula because we have to use it in order to get what we are looking for.