Topic explanation

Standard explanation

Substitute u=sin x or cos x, solve the quadratic, reject values outside [-1,1], then find angles.

Key points

• Quadratic equations in one trig function
• rule
• worked example
• Quadratic equations in one trig function: Substitute u=sin x or cos x, solve the quadratic, reject values outside [-1,1], then find angles.
• CONCEPT AND RULE: Substitute u=sin x or cos x, solve the quadratic, reject values outside [-1,1], then find angles.
• METHOD: For quadratic equations in one trig function, identify the given information and required result. Se
• Substitute u=sin x or cos x, solve the quadratic, reject values outside [-1,1], then find angles.
• Worked pattern: 2sin²x-3sin x+1=0 gives sin x=1 or 12.

Labelled diagram