Trig equations
Practice Flashcards
Why do trig equations have several solutions?
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All Flashcards in Topic 3.8
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3.8.19 cards
Why do trig equations have several solutions?
sin, cos and tan are periodic, so they hit the same value repeatedly.
After the first solution, how do you get the others for sin x = k?
Use x and 180° − x (then add periods if needed).
Second solution pattern for cos x = k?
x and 360° − x.
Second solution pattern for tan x = k?
x and x + 180°.
How do you solve sin(2x) = k over an interval?
Solve for 2x over the doubled interval, find all solutions, then divide each by 2.
How many solutions does sin(2x) = k give on 0°–360°?
Up to four (the doubled interval 0°–720° gives twice as many).
How do you solve 2sin²x − sin x − 1 = 0?
Let s = sin x, factor (2s+1)(s−1)=0, then solve sin x = each value.
What if the equation mixes sin² and cos?
Use cos²x = 1 − sin²x (or vice versa) to get one ratio, then it's a quadratic.
Paper 2 method for trig equations?
Graph each side and use intersect (or graph the difference and find zeros) over the interval.
Topic 3.8 study notes
Full notes & explanations for Trig equations
Math AA SL exam skills
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