The sine and cosine rules
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The sine rule for sides
Each side over the sine of its opposite angle is constant.
The sine rule for angles
The rule flipped to find an angle.
The cosine rule for sides
c² = a² + b² − 2ab cos C for the side facing a known included angle.
The cosine rule for angles
The cosine rule rearranged to find any angle from three sides.
The area formula ½ab sin C
Half the product of two sides and the sine of the included angle.
Choosing between the rules
Deciding from the given sides and angles whether right-angled trigonometry.
Practice
Practice
The sine rule for sides
Each side over the sine of its opposite angle is constant.
PracticeThe sine rule for angles
The rule flipped to find an angle.
PracticeThe cosine rule for sides
c² = a² + b² − 2ab cos C for the side facing a known included angle.
PracticeThe cosine rule for angles
The cosine rule rearranged to find any angle from three sides.
PracticeThe area formula ½ab sin C
Half the product of two sides and the sine of the included angle.
PracticeThe sine and cosine rules review
Sides, angles and areas in non-right-angled triangles.