Doubling angles, halving work

Mathematics · Geometry · ages 16-17

Name ______________________ Date ____________

sin A = 0.6 and cos A = 0.8. What is sin 2A?
Answer: ______________
Derive sin 2A by writing it as sin(A + A). What results?
- 2 sin A cos A
- sin^2 A + cos^2 A
- 2 sin A
- sin A cos A
What is sin 2A equal to?
- 2 sin A cos A
- Sin squared A plus cos squared A
- 2 sin A plus 2 cos A
Sin 2A comes from the addition rule with both angles equal.
Circle one: True False
cos A = 0.8 for acute A. What is cos 2A?
Answer: ______________
Dividing by sin x keeps every solution.
Circle one: True False
To remove sin^2 x from an equation, which rearrangement helps?
- sin^2 x = (1 + cos 2x)/2
- sin^2 x = 2 cos^2 x - 1
- sin^2 x = cos 2x
- sin^2 x = (1 - cos 2x)/2
Maya says cos 2A = 2cos^2 A − 1 clears sine from an equation. Is Maya right?
Circle one: True False
Which angles solve sin 2x equals sin x in a full turn?
- 0, 60, 180, and 300 degrees
- 30, 90, 210, and 270 degrees
- 0 and 180 degrees only
sin A = 0.28 and cos A = 0.96. What is sin 2A?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

0.96 · 2 × 0.6 × 0.8 = 0.96.
2 sin A cos A · Addition gives sin A cos A twice. The single product option drops the doubling.
2 sin A cos A · Doubling collects the two equal terms from sin of A plus A.
True · Setting B to A turns the sum rule into the double rule.
0.28 · 2 × 0.64 − 1 = 0.28.
False · It deletes the solutions where sin x is zero.
sin^2 x = (1 - cos 2x)/2 · From cos 2x = 1 − 2sin squared. The plus version belongs to cos squared.
True · That form contains no sine at all.
0, 60, 180, and 300 degrees · Each factor contributes its angles, and together they make four.
0.5376 · 2 × 0.28 × 0.96 = 0.5376.