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Unit Circle

CONCEPTS

Properties of a Unit Circle

• When given a value for cos, sin, or tan, recall there are certain angle ranges where the result is positive or negative

• The radius of the unit circle = 1

• The sign of cos, sin, and tan can be found by drawing the angle on the circle and then use the signs as referenced by the axis at 90°, 180°, 270°, and 360°



PRACTICE PROBLEMS

Question 1 If 180° < θ < 270° and sin θ = -12/13, then cos θ = ?


-- Answer -- -5/13

sin θ and cos θ are both negative between 180° to 270°



Question 2 When sin θ = -1, the value of cos θ = ?


-- Answer -- 0°

sin 0° = 0 => cos 0° = 1

sin 90° = 1 => cos 90° = 0

sin 180° = 0 => cos 180° = -1

sin 270° = -1 => cos 270° = 0

ACT PRACTICE PROBLEMS

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