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Topic 4: Trigonometry and functions

Sketching graphs

3 hours

• Use and apply the notation |x| for the absolute value for the real number x and the graph of y = |x|.
• Understand and use the relationship between the graph of y = f(x) and the graphs of y = 1/f(x), y = |f(x)| and y = f(|x|). 2 interactives

The reciprocal trigonometric functions, secant, cosecant and cotangent

3 hours

• Define and use the reciprocal trigonometric functions to determine their simplified exact values and sketch their graphs. 1 interactive

Trigonometric identities

6 hours

• Prove and apply the Pythagorean identities.
• Prove and apply the angle sum, difference and double-angle identities for sines and cosines.
• Prove and apply the identities for products of sines and cosines expressed as sums and differences.
• Convert sums a cos(x) + b sin(x) to R cos(x ± α) or R sin(x ± α) and apply these to sketch graphs. 1 interactive
• Model and solve problems that involve equations of the form a cos(x) + b sin(x) = c.
• Prove and apply multi-angle trigonometric identities up to angles of 4θ using the identities listed above, e.g. cos(4θ) = 8 cos⁴(θ) − 8 cos²(θ) + 1 and cosec(2θ) − cot(2θ) = tan(θ).