MATHEMATICS S5 UNIT 5: Trigonometric Functions and Their Inverses.

What Will You Learn?

• Precisely define sine, cosine, tangent, cosecant, secant, and cotangent using both the right-angle triangle (SOH CAH TOA) and the unit circle definitions.
• Evaluate trigonometric functions for special angles (e.g., 0,π/6,π/4,π/3,π/2, and their multiples) without a calculator, and for other angles using a calculator.
• Identify and articulate the domain, range, and periodicity for all six trigonometric functions.
• Recognize and interpret amplitude, phase shift, and vertical shift in transformed trigonometric functions (e.g., y=Asin(Bx−C)+D).
• Identify and understand the significance of asymptotes for tangent, cotangent, secant, and cosecant functions.
• Accurately sketch the graphs of the basic sine, cosine, and tangent functions.
• Graph transformed trigonometric functions, correctly applying concepts of amplitude, period, phase shift, and vertical shift.
• Interpret information about periodic phenomena from their trigonometric graphs.
• Apply trigonometric functions to find unknown side lengths or angles in right-angled triangles.
• Solve real-world problems involving angles of elevation/depression, bearings, and basic surveying.
• Understand the Need for Inverse Functions: Explain why the domains of trigonometric functions must be restricted to define their inverses (due to their periodic nature).
• Define and State Principal Value Ranges: Accurately define arcsine, arccosine, and arctangent (along with arccosecant, arcsecant, and arccotangent), including their specific principal value ranges.
• Evaluate exact values of inverse trigonometric functions for common inputs
• Graph Inverse Trigonometric Functions: Sketch the graphs of the principal branches of arcsine, arccosine, and arctangent, understanding their domain and range.
• Apply Inverse Functions in Problem Solving: Use inverse trigonometric functions to find angles in various geometric and applied contexts