How do we solve linear trigonometric equations?

Linear Trigonometric equations is a basic algebra problem such as:

3x+5=17

Just how we solve the algebra problem above by isolating the x, we do the same for trigonometric equations. However, the only difference of these equations is the memorization of the value of angles. 

For example: 

sin(x)+2=3 for 0° < x < 360°

We solve this equation just like an algebra equation. We subtract 2 from both sides and we should get sin(x)=1. This is where remembering the value of certain angles come in handy. If you do not remember the value of these angles, you can use your calculator to find out what is the value of sin(x)=1. You use arcsin in order to find out the value. This will appear like this on your calculator: sin-¹.You find the arcsin of 1 which is 90°. Than, you must find the reference angles which equal 1 as well. However, in this case the question above asks angles between 0 and 360. Therefore, the only angle that equals sin(x)=1 is 90°.

Viola! Thats how you solve Trigonometric Equations! 

Try this: 

                             2cos(2x)+1=0

Ever wondered how to convert Radians from Degrees and vice versa?

First off, what exactly is a radian?
Well, a radian is a unit of an angle which is equal to the central angle of a circle whose arc is is equal to the length of the radius.

This is exactly what I mean,

However, there is way to convert radians to degrees it is simple! In a full circle there are 2 Pi radians, therefore in half a circle (180 degrees) there are Pi radians. So in the radian measurement Pi radians is 180 degrees.

So that leaves us to this formula on converting Degrees to Radians:

And to convert Radians into degrees this shall be the formula: 

And Viola! Thats all you have to do, plug in whatever the angular measure and you are done!

Now try this:

Convert 15 Degrees: 

Convert 5Pi/6 Radians: 

Why is the name Pythagorean Identity is appropriate?

We all know that the Pythagorean theorem is written or drawn like this:

a² + b² = c²

^{The Pythagorean Identity used in Trigonometry is very similar to the Pythagorean Theorem. As we learned before, the Pythagorean Identity is:}

 Sin²x+Cos²x=1

Now lets use the same triangle with numbers: 

The Pythagorean Theorem will look like: (3)(3)+(4)(4)=(5)(5)

or 9+16=25

Now using the Pythagorean Identity: 

We have to plug in for Sin²x and Cos²x. So, Sin of x is 3/5 and Cosine of x is 4/5. However, both Sin and Cosine is raised to the second power so we square Sin and Cosine:

(3/5)(3/5)+(4/5)(4/5)

(9/25)+(16/25)=25/25,

and....

25/25=1!

Tada !!

The Pythagorean Identity is an appropriate name for it because when you plug the numbers in the Pythagorean Theorem just how it is formulated (remember Sin and Cosine were raised to the second power, don't forget to raise it to the second power!) you will result in 1, ALL THE TIME! 

If you forget the Pythagorean Identity, remember the Pythagorean theorem and you will succeed in trigonometry!