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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 · 15 questions

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1.Write down the exact value of sin 45°.
(a)√3/2
(b)√2/2
(c)1/2
(d)1
2.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.
(a)sin 30°, cos 30°, tan 30°
(b)cos 30°, tan 30°, sin 30°
(c)tan 30°, sin 30°, cos 30°
(d)sin 30°, tan 30°, cos 30°
3.Write down the exact value of sin 0°.
(a)1/2
(b)0
(c)1
(d)undefined
4.Triangle DEF has a right angle at E. Angle DFE = 60° and EF = 9 cm. Work out the exact length of DE.
(a)18 cm
(b)3√3 cm
(c)9√3/2 cm
(d)9√3 cm
5.Work out the exact value of (sin 30°)² + (cos 30°)².
(a)1/4
(b)3/4
(c)−1/2
(d)1
6.Write down the exact value of tan 0°.
(a)0
(b)1
(c)1/√3
(d)√3
7.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
8.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
9.Work out the exact value of cos 0° − sin 30°.
(a)1/2
(b)−1/2
(c)3/2
(d)1
10.Write down the exact value of tan 45°.
(a)0
(b)√3
(c)√3/3
(d)1
11.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
12.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
13.Work out the exact value of (cos 45°)² + (sin 45°)².
(a)2
(b)√2
(c)1
(d)1/2
14.Write down the exact value of cos 60°.
(a)0
(b)1
(c)1/2
(d)1/3
15.A right-angled triangle has a hypotenuse of 14 cm. One of the other angles is 30°. Work out the exact length of the side opposite the 30° angle.
(a)28 cm
(b)7 cm
(c)7√3 cm
(d)14/√3 cm

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