Trigonometric Identities

Moving on to the third unit, we discussed a very challenging lesson on how to prove Trigonometric Identities.

First, we did a recap about the eight trigonometric identities (Pythagorean and Reciprocal)

Pythagorean/Main Identities:

☻cos²θ + sin²θ = 1 ---> dividing both sides by cos²θ and by sin²θ, you'll get:

☻1 + tan²θ = sec²θ and ☻1 + cot²θ = csc²θ respectively.

Reciprocal/Basic Identities:

☻sinθ = 1/cscθ ☻cscθ = 1/sinθ

☻cosθ = 1/secθ ☻secθ = 1/cosθ

☻tanθ = 1/cotθ ☻cotθ = 1/tanθ

Next, in order to prove equations using identities, you must:

1. Use basic identity substitution.

2. Change everything to sine or cosine

3. Simplify all complex fractions into simple fraction.

4. Use fraction rules for addition and subtraction.

5. Factor if exponents are not the same on both sides.

Lastly, here are some important things to consider in this unit:

1. Familiarize yourself with all the 8 trig. identities. The better you know them, the easier it will be to recognize what is going on in the problems.

2. Work on the most complex side and simplify it so that it has the same form as the simplest side.

3. Don't work on both sides of the equation and try to meet in the middle. Start on one side and make it look like the other side.

4. In most examples where you see power 2 (that is, ²), it will involve using the Pythagorean identities or their derivatives.

Feel free to post a comment if there are points or clarifications you might want to add!

Carpe diem!