Grade 11 Trigonometry

Identities and reduction formulae, trig equations, and the sine, cosine and area rules in two dimensions.

Gr 11 Term 2 - TrigonometryTerm 2 and Term 3 - 6 weeks (CAPS)

Practise Trigonometry in the app →

What gets asked

• Simplify an expression using the square and quotient identities.
• Reduce ratios of $180^{\circ }\pm \theta$ and $360^{\circ }-\theta$ and evaluate exactly.
• Solve a trig equation on a stated interval.
• Use the sine, cosine and area rules in triangles without right angles.

You must be able to

• Reach for ${\sin }^2\theta +{\cos }^2\theta =1$ whenever squares appear.
• Reduce to the acute reference angle, then attach the quadrant sign.
• After the reference angle, place every solution the interval allows.
• Sine rule pairs a side with its opposite angle; cosine rule takes two sides and the included angle.

Traps that cost marks

• Stopping at the calculator angle when solving $\sin x=0,5$ on $[0^{\circ };360^{\circ }]$. Sine is positive in two quadrants: $x=30^{\circ }$ or $x=150^{\circ }$.
• Adding the $2ab\cos C$ term in the cosine rule. The rule subtracts it: $c^2=a^2+b^2-2ab\cos C$.
• Pairing a side with an adjacent angle in the sine rule. Each fraction pairs a side with the angle OPPOSITE it.

Worked example