Extended Trigonometry

Topics

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Sample objectives

What this unit covers

• Right-angled triangles: Understand and apply the sine, cosine, and tangent ratios for acute angles in right-angled triangles, with angles provided in degrees and answers expressed in degrees to one decimal place. Solve two-dimensional problems using Pythagoras' theorem and trigonometry, which may involve bearings. Recognize that the shortest distance from a point to a line is the perpendicular distance. Perform calculations related to angles of elevation and depression.
• Exact trigonometric values: Understand the precise values of sine and cosine for angles 0°, 30°, 45°, 60°, and 90°, as well as the tangent values for angles 0°, 30°, 45°, and 60°.
• Trigonometric functions: Identify, draw, and analyze the graphs of the following functions for angles between 0° and 360°: y = sin x, y = cos x, and y = tan x. Solve equations involving sin x, cos x, or tan x within the range of 0° to 360°, such as sin x = 2 or 2 cos x + 1 = 0.
• Non-right-angled triangles: Apply the sine and cosine rules to solve problems related to non-right-angled triangles, including those with obtuse angles and ambiguous cases. Use the formula for the area of a triangle, which is given as area = ab sin C.
• Pythagoras’ theorem and trigonometry: Use Pythagoras’ theorem and trigonometry to perform calculations and solve problems in three-dimensional space, including finding the angle between a line and a plane.