How can you find out the relationships of triganometry functions?

Question: What are trigonometry functions and how can we identify them?

Answer: 

Trigonometric functions are functions that help relate sides of a triangle to its angles expressed through adjacent, hypotenuse and opposite, which is shown on the triangle below.

The trigonometric functions are: 

 The reciprocal functions of sine, cosine and Tangent is:

 

As you can see the reciprocals of sine, cosine and tangent is the opposite of their appointed trig function, or their trig function turned over.

 Lets try a Question:

What is the co function(Reciprocal function)of the trig function below:

Tangent(Tan): 4/5

The answer is Cot: 5/4 

the reason is because the trig function of tangent is opposite/ adjacent, since we are trying to find the reciprocal function we need to flip Tan over creating 5/4 or adjacent over hypothesis.

Try it Yourself:

What is the co functions of the trig functions below:

Cotangent: 8/10

Co secant: 5/ 8

Secant: 3/6

How to graphconvert degrees into radians and vice versa?

Question: How do to convert  degrees to radians and vice versa?

In order to turn a degree as simple as 90 into a radian of π/2

The main thing that you need to know when trying to change degrees into radians, is that the degrees has to be multiplied by the formula π /180. 

For example: Convert 48 degrees into a radian?

Step 1: Multiply

π/180* 48

=48π/180 

Step 2: Simplify

48π/180  / 4/4

= 12π/45

So the finale answer is 12π/45

In order to find howto convert radians into degrees all that you have to do is flip π/180 over which will make 180/π.

For example: Convert 3π/2 into degrees? 

Step 1: Multiply 

3π/2 * 180/ π

Step 2: cancel out the two π's, which will leave...

3/2* 180

Step 3: Multiply 3 and 180 

540/2

Step 4: Divide

270

The final answer is 270

Try it yourself:

1. Convert 126 degrees  into a radian?

2. Convert 4π/2 into degrees?

Pythagorean Identity and why is it necessary/

Question: What is the Pythagorean Identity and why is it necessary

Pythagorean Identities definition:

It is known that any point on a unit circle can be represented by sin θ and cos θ making it possible to draw a triangle with one side the length of  sin θ and another the length of  cos θ and the last side which will naturally be 1 by definition.  With this description the first or original Pythagorean identity is sin^2 θ+cos^2 θ=1.  As you can see this equation kind of resembles the Pythagorean theorem which is a^2+b^2= c^2, because the Pythagorean Identity is the application of the Pythagorean theorem but to a unit circle as described in the picture to the left.

The three Pythagorean Identities: 

The first Pythagorean Identity is as we mentioned before  sin^2θ+cos^2θ=1.  The second Pythagorean theorem  of Tan^2θ +1= sec^2θ and the third Pythagorean identity is 1+cot^2θ=csc^2θ.

Importance of Pythagorean identities and why this name is appropriate:      

The reason why the Pythagorean identities is important is because if you are working on a problem using the unit circle and had the value of a trig function such as cosine but wanted to find sine you will use either of the three Pythagorean Identities.   This identity is important because it sets an expression involving trig functions equal to 1, and this simplification is very helpful for solving equations. As such, this is probably one of the most frequently used trig identities. The word Pythagorean is used to describe the relationship between a^2+b^2=c^2 which applies to the right angle, while the word identity when applying to math means a relation that is true in every interpretation.  So together the word Pythagorean Identity means the relationship between a^2+b^2=c^2 that is true in every interpretation.  This definition and importance of the Pythagorean Identity shows the importance of this name in the way that the Pythagorean Identity has a identity of sin^2θ+cos^2θ=1 which is similar to a^2+b^2=c^2, because in a^2+b^2=c^2 it applies to a right triangle by itself while the Pythagorean Identities applies to unit circles which are different interpretations of each other.  Another example of how this definition applies to how appropriate the name Pythagorean Identity is all of the Pythagorean Identities are different forms of each other.