Sketch and analyze sine and cosine graphs with amplitude, period, phase shift. Math 30-1.
Lesson 4.5 of Trigonometric Ratios & Functions in Math 30-1 — Alberta curriculum lessons.
Before we jump into solving trigonometric equations, we need to build one important skill first: factoring trigonometric expressions.
In this tab, we will focus on how to factor trig expressions the same way you would factor regular algebraic expressions. Once you're comfortable factoring, solving the equations becomes much easier — because factoring breaks a complicated equation into smaller, simpler pieces you already know how to solve.
Second-degree trigonometric equations behave like quadratic equations.
We solve them using the same algebraic strategies:
• Set the equation equal to zero
• Factor the expression
• Solve each factor
Key Idea: Treat trigonometric ratios (sin, cos, tan, etc.) as if they were variables when factoring.
Factoring is the first step in solving second-degree trigonometric equations.
Once factored, we can use the Zero Product Property:
If AB = 0, then either A = 0 or B = 0.
This allows us to break a complex equation into simpler first-degree equations that we already know how to solve!
Example:
If x(1 + 2 x) = 0, then:
Either x = 0 OR 1 + 2 x = 0
We can solve each of these separately!
Second-degree trig equations contain a squared trig function such as:
^2 x, ^2 x, ^2 x
We solve them using the same steps as quadratic equations.
Factor: x + 2 x x
Solution:. Step 1: Identify the common factor
Look at both terms:
• First term: x
• Second term: 2 x x
The common factor is x.
Step 2: Factor out the common term
x + 2 x x = x(1 + 2 x)
Final Answer:
x(1 + 2 x)
Create a free Studyio account to take the full lesson with voice-over teaching, practice questions and instant feedback.