Sine and cosine of complementary angles
- One fraction, two names — 3 tasks
- Which side does which job — 3 tasks
- Sine and cosine of complements — 3 tasks
- Reading a sine–cosine equation — 3 tasks
- Going Deeper — 9 tasks
- Practice — 23 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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Where Is x? Sine and Cosine of Complementary Angles — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 pieces, each a sine-cosine statement with an unknown x, and nothing to solve. Students sort them: x is inside the angles, so the angles add to 90°; x is in the values of sin A and cos B, so the values are equal; or it is not the sine of one acute angle and the cosine of the other (two tangents, or one angle twice), so the rule says nothing.
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Add to 90 or Set Equal? Sine and Cosine of Complementary Angles — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page. Each sets a sine equal to a cosine with an unknown x. When x is inside the angles, the angles add to 90°; when x is in the values of sin A and cos B, the two values are equal. The wrong answers are the two opposite moves: setting the angles equal, or adding the values to 90. The row of box numbers at the foot is the check.
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Is sin A = cos B? Sine and Cosine of Complementary Angles — Mystery Picture 25–35 minutes · 5 sheets
25 squares, each a lettered right triangle with one statement under it, such as "sin P = cos R", and no numbers. Is the statement true? The white squares are the common mistakes: two sines, two tangents, one angle twice, the right angle used as an acute angle, and a triangle with no right angle marked. Fill or leave white, and a picture appears.
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Add to 90 or Set Equal? Sine and Cosine of Complementary Angles — Scavenger Hunt a full class period · 13 sheets
16 cards around the room. Each sets a sine equal to a cosine with an unknown x, in symbols or in words. When x is inside the angles, the angles add to 90°; when x is in the values of sin A and cos B, the values are equal; some cards then ask for an angle. Setting the angles equal, adding the values to 90, or stopping at x lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.