Solving quadratic trigonometric equations (HSC SSCE Mathematics Extension 1): Flashcards
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What is a quadratic equation?
What is a quadratic equation?
It is ax^2 + bx + c = 0, where a, b, c are numbers.
What are trigonometric functions?
What are trigonometric functions?
Functions like sin(x), cos(x), and tan(x) relate angles.
What is an extraneous solution?
What is an extraneous solution?
A solution that does not satisfy the original equation.
How to transform sin^2(x) in equations?
How to transform sin^2(x) in equations?
Replace sin^2(x) with y^2 for simplification.
What is the first step in solving sin^2(x) - 5sin(x) + 6?
What is the first step in solving sin^2(x) - 5sin(x) + 6?
Set y = sin(x) to simplify the equation.
What does cos(x) range between?
What does cos(x) range between?
Cosine values range from -1 to 1.
What is the quadratic formula?
What is the quadratic formula?
x = (-b ± √(b²-4ac)) / 2a.
What should you check after solving trig equations?
What should you check after solving trig equations?
Ensure solutions are within the valid range for trig functions.
What happens with extraneous solutions?
What happens with extraneous solutions?
They may arise due to the periodic nature of trig functions.
How to solve tan^2(x) - 4tan(x) = 0?
How to solve tan^2(x) - 4tan(x) = 0?
Factor to tan(x)(tan(x) - 4) = 0 and solve.