Week 13: Trigonometric Equations

This week, the blog subject was on Solving Trigonometric Equations which was lesson 4.9. 

We first looked at Steps to Solve Trigonometric Equations.

Step 1: Combine Like Terms: collecet adn combine all constants together and all like trig functions together

Step 2:Collect All Trig Terms on One Side of Equation: algebraically move all trig functions to one side of equation and all constants to other side

Step 3: Apply a Trig Identity (if Possible): somtimes it’s helpful to apply a trig identity in order to simplify the equation

Step 4: Factor (If Possible): sometimes it’s helpful to factor the equation. especially if there are powers to present greater than one

Step 5: Isolate the Trig Function: Get a trig function in all by itself on one side of the equation

Step 6: Solve for variable (may need to be inverse trig functions): sometimes it will be possible to find “easy” values that satisfy the euqation such as 30°, 45°, 60°, 90°, etc. Other times, we must use the inverse trig functions and a calculator to find solutions. 

Now how do you solve them?

Example 1: sinx=-cosx

sinx/cosx=-1

tanx=-1

tanx=x/y

Answers possible:

3π/4

7π/4

HINT: if you have two answers on the same line that crosses the origin. Take the first one as it is redundent to repeat it twice.

HINT #2: If that happens: the answer would have nπ after it. If that does not happen then 2nπ goes after it.

the answer then is 3π/4 +nπ.

Below are a few more examples:

This is what you do to solve Trigonometric Equations

SEE YOU NEXT WEEK!