Sine Half Angle

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1) If cos θ = 4/5 and θ is in quadrant I, find sin(θ/2).
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About This Quiz
Sine Half Angle - Quiz

Ready to take big angles and cut them in half? In this quiz, you’ll explore the half-angle formula for sine, simplify tricky expressions, and calculate exact values for special angles. You’ll also learn how quadrant signs affect your answers. Take this quiz to get comfortable with one of trig’s most... see moreuseful shortcuts. see less

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2) Derive the formula for sin(θ/2) from the double-angle identity for cosine.
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3) If θ = 120°, compute sin(θ/2) exactly.
Submit
4) If sin θ = 5/13 with θ in quadrant II, find sin(θ/2).
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5) Simplify (1 - cos θ)/2.
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6) Express tan(θ/2) in terms of sin θ and cos θ.
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7) If cos θ = 7/25 and θ is in quadrant IV, find sin(θ/2).
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8) Which statement is a geometric interpretation of the sine half-angle formula?
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9) Which formula correctly expresses sin(θ/2) in terms of cos θ?
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10) If θ = 300°, determine the sign of sin(θ/2).
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11) If cos θ = −12/13 and θ is in quadrant II, find sin(θ/2).
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12) Simplify sin²(θ/2) + cos²(θ/2).
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13) Which form is not equivalent to sin(θ/2)?
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14) If sin θ = 24/25 in quadrant I, compute sin(θ/2).
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15) Simplify (1 − cos 2θ)/2.
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16) If θ = 90°, find sin(θ/2).
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17) Which quadrant is θ/2 located in if θ = 200°?
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18) If cos θ = 0, compute sin(θ/2).
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19) If θ = 45°, compute sin(θ/2).
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20) Which application uses sine half-angle identities most often?
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If cos θ = 4/5 and θ is in quadrant I, find...
Derive the formula for sin(θ/2) from the double-angle identity for...
If θ = 120°, compute sin(θ/2) exactly.
If sin θ = 5/13 with θ in quadrant II, find sin(θ/2).
Simplify (1 - cos θ)/2.
Express tan(θ/2) in terms of sin θ and cos θ.
If cos θ = 7/25 and θ is in quadrant IV, find sin(θ/2).
Which statement is a geometric interpretation of the sine half-angle...
Which formula correctly expresses sin(θ/2) in terms of cos θ?
If θ = 300°, determine the sign of sin(θ/2).
If cos θ = −12/13 and θ is in quadrant II, find sin(θ/2).
Simplify sin²(θ/2) + cos²(θ/2).
Which form is not equivalent to sin(θ/2)?
If sin θ = 24/25 in quadrant I, compute sin(θ/2).
Simplify (1 − cos 2θ)/2.
If θ = 90°, find sin(θ/2).
Which quadrant is θ/2 located in if θ = 200°?
If cos θ = 0, compute sin(θ/2).
If θ = 45°, compute sin(θ/2).
Which application uses sine half-angle identities most often?
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