Inverse trigonometric ratios: finding an angle
- The table of ratios, read both ways — 4 tasks
- One number, three angles — 3 tasks
- From two sides to an angle — 6 tasks
- Two wrong answers that look right — 3 tasks
- Going Deeper — 6 tasks
- Practice — 24 tasks
- Summary — 7 tasks
- Cool-down — 3 tasks
Classroom activities
Things a class does rather than writes on. Each one is a finished PDF: print it, cut it up if it says so, and hand it round.
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Inverse Trig Ratios: Is θ Right? — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 triangles drawn to scale, each with the angle θ marked, side lengths and a value for θ. Students sort them: the value is right; it is wrong (the other acute angle, or the wrong inverse key); or nobody can tell, because no right angle is marked or only one side is given, even though it looks right.
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Which Key Finds θ? Inverse Trig Ratios — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a right triangle drawn to scale with two sides given and the angle θ marked. Students name the ratio, write it as a decimal, and use sin⁻¹, cos⁻¹ or tan⁻¹. The wrong answers are the two that exams use: the other acute angle, and the wrong key. The row of box numbers at the foot is the check.
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Read the Table Backward: Inverse Trig Ratios — Mystery Picture 25–35 minutes · 5 sheets
25 squares, each a sentence such as "the angle whose sine is 0.60 is between 35° and 40°", read from the printed table of ratios beside them. No calculator. Fill it if it is true, leave it white if not, and a picture appears. The false ones are the common mistakes: the wrong column, the neighbouring rows, a sine above 1.
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Inverse Trig Ratios: Find the Angle — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each a right triangle drawn to scale with two sides given and the angle θ marked. Groups form the ratio, write it as a decimal, use sin⁻¹, cos⁻¹ or tan⁻¹, and walk to the card showing θ to the nearest degree. Finding the other acute angle, or pressing the wrong key, lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.