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Flip to reveal answersWhy do trig equations have several solutions?
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All 9 Flashcards — Solving trig equations
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Question
Why do trig equations have several solutions?
Answer
sin, cos and tan are periodic, so they hit the same value repeatedly.
Question
After the first solution, how do you get the others for sin x = k?
Answer
Use x and 180° − x (then add periods if needed).
Question
Second solution pattern for cos x = k?
Answer
x and 360° − x.
Question
Second solution pattern for tan x = k?
Answer
x and x + 180°.
Question
How do you solve sin(2x) = k over an interval?
Answer
Solve for 2x over the doubled interval, find all solutions, then divide each by 2.
Question
How many solutions does sin(2x) = k give on 0°–360°?
Answer
Up to four (the doubled interval 0°–720° gives twice as many).
Question
How do you solve 2sin²x − sin x − 1 = 0?
Answer
Let s = sin x, factor (2s+1)(s−1)=0, then solve sin x = each value.
Question
What if the equation mixes sin² and cos?
Answer
Use cos²x = 1 − sin²x (or vice versa) to get one ratio, then it's a quadratic.
Question
Paper 2 method for trig equations?
Answer
Graph each side and use intersect (or graph the difference and find zeros) over the interval.
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Topic 3.8 hub
Trig equations
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