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Exact trigonometric values worksheet — GCSE Foundation

Fifteen questions on "exact trigonometric values" — DfE statement G21. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Exact trigonometric values worksheet — GCSE Foundation

Maths · GCSE Foundation · G21 · Exact trigonometric values · Non-calculator · 15 questions

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1.A pop-up canopy has two sloping supports that meet at the top. Each support makes an angle of 30° with the ground and is 6 m long. Using the exact value of cos 30°, work out the total width of the canopy's base.
(a)3√3 m
(b)6√3 m
(c)12 m
(d)6 m
2.A ramp rises at 30° to the horizontal. Its sloping surface is 4.8 m long. Safety rules say the vertical rise of a ramp must be no more than 2.5 m. Work out how far below that limit the rise of this ramp is.
(a)0.1 m
(b)2.4 m
(c)7.1 m
(d)0.9 m
3.Three of these are rational numbers and one is irrational. Write down the one that is irrational.
(a)sin 30°
(b)tan 0°
(c)cos 45°
(d)sin 90°
4.A zip-wire is fixed at an angle of 60° to the horizontal ground. The zip-wire is 12 m long. Using the exact value of cos 60°, work out the exact horizontal distance it covers.
(a)24 m
(b)4√3 m
(c)6√3 m
(d)6 m
5.Work out the exact value of tan 30° + tan 30°.
(a)2√3/3
(b)√3/3
(c)√3
(d)2√3
6.Write down the exact value of sin 0°.
(a)1/2
(b)0
(c)1
(d)undefined
7.A kite string makes an angle of 30° with the ground. The kite is flying at a height of 6 m directly above a point on the ground. Using the exact value of sin 30°, work out the exact length of the kite string.
(a)4√3 m
(b)12 m
(c)6√3 m
(d)3 m
8.Write down the exact value of cos 60°.
(a)0
(b)1
(c)1/2
(d)1/3
9.Work out the exact value of cos 0° − sin 30°.
(a)1/2
(b)−1/2
(c)3/2
(d)1
10.Work out the exact value of sin 30° + cos 60°.
(a)0
(b)√3
(c)1
(d)1/2
11.Write down the exact value of cos 45°.
(a)1/2
(b)√2/2
(c)√3/2
(d)√2
12.Write down the exact value of tan 45°.
(a)0
(b)√3
(c)√3/3
(d)1
13.Work out the exact value of (cos 45°)² + (sin 45°)².
(a)2
(b)√2
(c)1
(d)1/2
14.Work out the exact value of sin 45° × cos 45°.
(a)√2
(b)1
(c)1/2
(d)√2/2
15.Write down the exact value of sin 60°.
(a)1/2
(b)√2/2
(c)√3/2
(d)√3

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