Practice IB Mathematics Applications & Interpretation (AI) Topic AHL 3.8—unit Circle, Pythag Identity, Solving Trig Equations Graphically with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 3.8—unit Circle, Pythag Identity, Solving Trig Equations Graphically and mirrors Paper 1, 2, 3 style where relevant.
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The point lies on the unit circle and corresponds to an angle , where . The coordinates of are
Find the value of .
Write down the values of and .
Solve the equation for , where is in radians.
Consider the trigonometric function , where is measured in radians, over the interval .
Sketch the graph of over the interval .
Using your graph, estimate the solutions of the equation within the interval .
Let , where is measured in radians and .
Find .
Hence find the values of for which .
A triangular garden plot has two sides of length 20 m and 12 m. Let be the included angle. The area is m.
Verify that .
Determine both possible lengths for the third side of the plot.