Matching sin and cos
Cut out each of the 18 cards below. Arrange them into four sets of four, showing …
a. a diagram of a triangle
b. the sine value
c. the cosine value
d. the ratio of the given sides.
You will have two cards left over, which both fit into one of the sets. Which set do they
fit into? Explain how you know.
0.8
cos 36.9°
sin 30°
0.38
cos 60°
0.5
2
1
30°
1
√2
sin 53.1°
45°
10
53.1°
sin 45°
1
8
5
sin 22.6°
cos 45°
cos 67.4°
0.71
© www.teachitmaths.co.uk 2012
17054
13
22.6°
tan 45°
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Matching sin and cos
Teaching notes
This resource helps students understand that, in a right-angled triangle, the sine of one
angle is equal to the cosine of the other (non 90°) angle.
A useful extension is to ask students to come up with their own set of cards for other
students to try, this time showing the cosine ratio in the diagram.
Answers
2
1
30°
sin 30°
cos 60°
0.5
10
53.1°
8
sin 53.1°
cos 36.9°
0.8
5
22.6°
13
sin 22.6°
cos 67.4°
1
0.38
√2
45°
sin 45°
cos 45°
0.71
tan 45° and 1 also fit into this set – it is an isosceles triangle.
© www.teachitmaths.co.uk 2012
17054
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