Unit circle, exact values & solving trig equations
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Flip to reveal answersOn the unit circle, what are the coordinates of the point at angle θ?
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All 8 Flashcards — Unit circle, exact values & solving trig equations
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Question
On the unit circle, what are the coordinates of the point at angle θ?
Answer
(cos θ, sin θ) — cos is the x-coordinate (across), sin is the y-coordinate (up).
Question
Why are sin θ and cos θ always between −1 and 1?
Answer
They're coordinates of a point on a circle of radius 1, so neither can exceed the radius.
Question
State the Pythagorean identity.
Answer
sin²θ + cos²θ = 1 (it's Pythagoras applied to the unit-circle point).
Question
Exact value of cos 60° and sin 60°?
Answer
cos 60° = ½, sin 60° = √3⁄2.
Question
Exact value of sin 45° and cos 45°?
Answer
Both equal √2⁄2 (≈ 0.707).
Question
How do you express tan θ using sin and cos?
Answer
tan θ = sin θ / cos θ.
Question
Given cos θ = 0.6 and θ acute, find sin θ.
Answer
sin²θ = 1 − 0.36 = 0.64, so sin θ = 0.8 (positive in Quadrant 1).
Question
How do you solve a trig equation over a given interval on the GDC?
Answer
Graph both sides over the interval, use 'intersect' to read EVERY crossing, then keep only solutions inside the interval.
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Unit circle & trig equations (HL only)
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