Trigonometry Identities: Mixed Practice

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1) Which formula expresses sin(θ/2)?
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Trigonometry Identities: Mixed Practice - Quiz

Can you put it all together? In this final quiz, you’ll tackle sine, cosine, and tangent half-angle identities side by side. From proofs and simplifications to exact evaluations and quadrant checks, it’s a full workout for your half-angle skills. Take this quiz to test your mastery across all the identities.

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2) Which formula expresses cos(θ/2)?
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3) Which formula expresses tan(θ/2)?
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4) If cosθ = 4/5 and θ is in quadrant I, find sin(θ/2).
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5) If cosθ = 3/5 and θ is in quadrant IV, find cos(θ/2).
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6) If sinθ = 24/25 (quadrant I), find cos(θ/2).
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7) If tan(θ/2) = 2/3, find cosθ.
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8) If tan(θ/2) = 2/3, find sinθ.
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9) Evaluate tan(22.5°) exactly.
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10) Evaluate cos(22.5°) exactly.
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11) Evaluate sin(22.5°) exactly.
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12) Simplify cos²(θ/2) in terms of θ.
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13) Simplify sin²(θ/2) in terms of θ.
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14) If cosθ = 0 and 0 < θ < π, compute cos(θ/2).
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15) If θ is in quadrant II and cosθ = −12/13, find sin(θ/2).
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16) If θ = 300°, determine the sign of sin(θ/2).
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17) If sin(θ/2) = 3/5 and θ/2 is in quadrant I, find cosθ.
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18) If cos(θ/2) = 3/5 and θ/2 is in quadrant I, find cosθ.
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19) If θ = 60°, compute tan(θ/2).
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20) If 0 < θ < π and cosθ = 0.6, find sin(θ/2) in simplest radical form.
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Which formula expresses sin(θ/2)?
Which formula expresses cos(θ/2)?
Which formula expresses tan(θ/2)?
If cosθ = 4/5 and θ is in quadrant I, find sin(θ/2).
If cosθ = 3/5 and θ is in quadrant IV, find cos(θ/2).
If sinθ = 24/25 (quadrant I), find cos(θ/2).
If tan(θ/2) = 2/3, find cosθ.
If tan(θ/2) = 2/3, find sinθ.
Evaluate tan(22.5°) exactly.
Evaluate cos(22.5°) exactly.
Evaluate sin(22.5°) exactly.
Simplify cos²(θ/2) in terms of θ.
Simplify sin²(θ/2) in terms of θ.
If cosθ = 0 and 0 < θ < π, compute...
If θ is in quadrant II and cosθ = −12/13, find sin(θ/2).
If θ = 300°, determine the sign of sin(θ/2).
If sin(θ/2) = 3/5 and θ/2 is in quadrant I, find cosθ.
If cos(θ/2) = 3/5 and θ/2 is in quadrant I, find cosθ.
If θ = 60°, compute tan(θ/2).
If 0 < θ < π and cosθ = 0.6, find sin(θ/2)...
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