Sine & cosine rules
Practice Flashcards
State SOH-CAH-TOA.
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All Flashcards in Topic 3.2
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3.2.19 cards
State SOH-CAH-TOA.
sin θ = opp/hyp, cos θ = adj/hyp, tan θ = opp/adj.
Which side is the hypotenuse?
The longest side, opposite the right angle.
How do you find a side with right-angled trig?
Pick the ratio linking the angle, the wanted side and a known side; rearrange for the unknown.
How do you find an angle from two sides?
Form the ratio, then take the inverse (sin⁻¹, cos⁻¹, tan⁻¹).
When do you use Pythagoras instead of trig?
When you have two sides and need the third with no angle involved.
Side opposite 30° when hypotenuse is 10?
10 sin 30° = 5.
Angle with opposite 3, adjacent 4?
tan⁻¹(3/4) ≈ 36.9°.
Common right-angled-trig mistake?
Calculator in the wrong mode (degrees vs radians), or mislabelling opp/adj.
Hypotenuse from legs 5 and 12?
√(25 + 144) = 13.
3.2.29 cards
State the sine rule.
a/sinA = b/sinB = c/sinC (side over the sine of its opposite angle).
State the cosine rule for a side.
a² = b² + c² − 2bc·cosA, with A opposite a.
Cosine rule rearranged for an angle?
cos A = (b² + c² − a²)/(2bc).
When do you use the sine rule?
When you have a side with its opposite angle, plus one more side or angle.
When do you use the cosine rule?
For SAS (two sides + included angle → third side) or SSS (three sides → an angle).
How do you use the sine rule to find an angle?
Flip it: sinA/a = sinB/b, so the unknown sine is on top.
Why is the cosine rule 'Pythagoras with a correction'?
When A = 90°, cosA = 0 and a² = b² + c².
No side–opposite-angle pair — which rule first?
The cosine rule — it usually gives you a pair to then use the sine rule.
SAS triangle: b=7, c=9, A=60°. Find a.
a² = 49 + 81 − 2·7·9·½ = 67 ⇒ a ≈ 8.19.
3.2.38 cards
Area of a triangle with two sides and the included angle?
½ab·sinC, where C is the angle between sides a and b.
Which angle goes in ½ab·sinC?
The included angle — the one between the two sides you use.
How do you find the included angle from a given area?
Set ½ab·sinC = Area, solve for sin C, then take sin⁻¹ (watch for the obtuse solution).
Why might there be two possible included angles?
sin C = sin(180° − C), so an acute and an obtuse angle can give the same area.
Area of a triangle: sides 6, 8, included angle 30°?
½(6)(8)sin30° = 12.
What if the included angle isn't given?
Find it first (cosine rule from SSS, or sine rule), then use ½ab·sinC.
Is ½ab·sinC ever just ½ab?
Yes, when C = 90° (sin 90° = 1) — it reduces to ½ × base × height.
Common area-formula mistake?
Using a non-included angle, or forgetting the factor of ½.
Topic 3.2 study notes
Full notes & explanations for Sine & cosine rules
Math AA SL exam skills
Paper structures, command terms & tips
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