Trigonometric ratios defined by similarity
- What survives a photocopy — 3 tasks
- The angle a right triangle gets for free — 3 tasks
- One angle, one number — 6 tasks
- Naming the three ratios — 6 tasks
- Reading the values both ways — 6 tasks
- Practice — 24 tasks
- Summary — 2 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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Sine, Cosine, or Not a Right Triangle? Trigonometric Ratios — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 pieces, each a lettered triangle with an arc at one angle and a fraction of two of its sides, and no numbers. Students sort them: the fraction is the sine of the marked angle, the cosine, or the triangle has no right-angle mark, so neither can be used. The triangles are turned every way, so the opposite and adjacent legs must be found from the arc, not from the page.
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Opposite or Adjacent? Sine, Cosine and Tangent — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page. Each is a small turned right triangle with its three sides and an arc at one acute angle, and asks for the sine, cosine or tangent of that angle as a fraction. The wrong answer in every box comes from swapping the opposite and adjacent legs, which gives the ratio of the other acute angle. The row of box numbers at the foot is the check.
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Sine, Cosine or Tangent: Is It True? Trigonometric Ratios — Mystery Picture 25–35 minutes · 4 sheets
25 squares, each one equation such as sin P = QR/PR, written with the letters of one of five turned right triangles: fill the square if the equation is true, leave it white if it is not. There are no numbers, so the only way through is to name the opposite leg, the adjacent leg and the hypotenuse for the angle each equation names. The white squares are the mistakes students really make: opposite and adjacent swapped, the hypotenuse used as the adjacent leg, and a ratio written upside down. When every square is right, a picture appears.
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Sine, Cosine and Tangent: Find the Ratio. Trigonometric Ratios — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each one turned right triangle with its three sides printed and an arc at one acute angle. The card asks for the sine, cosine or tangent of that angle as a fraction of two side lengths. Swapping the opposite and adjacent legs lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.