How to find the sum and the products of the roots and the axis of symmetry?

Question: How do we find the sum and the product of roots?

Answer:

Let's use a example problem in order to find both the sum and products of roots:

Example problem:

2x^2+ 4x- 16

In order to find the product of this equation we need to use the formula: c /a

In order top make plugging in this formula seem easier we need to use ax^2+bx-c which can apply to the formula already stated. 

So that means that  c= -16 and a=2

so the product of this equation is -8 because -16/2= -8

Now for the sum of the roots, the formula that we will use is: -b / a

So this means that -b= -4 and a=2

So the sum of the roots of this equation is -2 because -4/2 = -2

In order to find the axis of symmetry of this equation all that we are doing is that we are plugging the numbers in the equation into -b/2a

Which means that -b=-4 and a=2

which also means that the axis of symmetry is -1, because -4/2(2)= -1

Now try this yourself:

What is the axis of symmetry and the sum and product of the roots of the equation below?

5x^2+10x+25

How do we solve recipical trigonometric identities?

Question: How do we simplify a trig function into a single trig function without a denominator?

Here are the steps:

Step 1. Convert everything in the problem to sin(x) and cos(x)

Step 2. Now use K, F, C or Keep, Flip and Change 

Step 3. Now multiply across as you would a normal division problem.

Step 4. And BAMMMM! there is your finale answer. In some cases you may have to convert to the recipicals of Sin, Cos and Tangent (Csc, Sec and Cot)

In case you still don't understand how to simplify a trig function, Let us use a actual problem using these steps:

Problem: Sec(x)/ Cos(x)

Step 1:  1/Cos(x)/ Cos(x)

Step 2: 1/Cos(x)* 1/Cos(x)

Step 3: 1/Cos^2(x)

Step 4:  Sec^2(x)

Now Try it yourself: 

Cot^2(x)/ Csc^2(x)




Cite: http://www.deltamath.com/student.html#a

How to convert Radians into degrees?

Question: How do we convert Radians into degrees?

Answer:

In order to find how to convert radians into degrees all that you have to do is flip π/180 over which will make 180/π as shown in the post before.

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 4π/2 into degrees?

How do we solve Linear Trigonometric Equations?

Question: How do we solve Linear Trigonometric Equations?

Answer:

Linear Trignometric equations will look like this:Find all angles, 0≤A<360, that satisfy the equation below, to the nearest 10th of a degree.

So for the equation: 3TanA-7= TanA-8

In order to sole Linear Trig equations as shown above follow these steps.

Step 1: Substitute the tri function(TanA) with a variable of x to make solving easier:

3x−7

=

x−8

Step 2: Now solve like a regular equation, bringing the constant(7) to the right side:

3x−7	=	x−8
−x−7	=	−x
2x−7	=	−8
+7	=	+7

Step 3: Now divide by the coefficient(2) of x: 

2x2	=	−12
x	=	−12

Step 4: Now plug in the trig function back in for x:

tanA

=

−12

Step 5: Now determine the quadrants were TanA is negative in order to find the reference angle:(All-Students-Take-Calculus)

Tan is negative in quadrants II and IV

In order to find the reference angle  we need to plug in the -1/2  using the invere of tan as shown below

tan−1(12)=26.57≈26.6∘
Step 6: Plug in the reference angle of 26.6 as shown below: 

Quads: II, IVRef: 26.6∘ AII=180−26.6=153.4∘ AIV=360−26.6=333.4∘ TRY IT YOURSELF: Find all angles, 0≤A<360, that satisfy the equation below, to the nearest 10th of a degree. 9sinB−2 = sinB−8

x−8

Cites: http://www.deltamath.com/student.html#a