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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.Work out the exact value of sin 45° × cos 45°.
(a)√2
(b)1
(c)1/2
(d)√2/2
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 cos 60°.
(a)0
(b)1
(c)1/2
(d)1/3
4.Work out the exact value of cos 0° − sin 30°.
(a)1/2
(b)−1/2
(c)3/2
(d)1
5.Write down the exact value of tan 0°.
(a)0
(b)1
(c)1/√3
(d)√3
6.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
7.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
8.A tent's sloping side makes an angle of 45° with the ground. The sloping side is 3√2 m long. Using the exact value of sin 45°, work out the exact height of the tent.
(a)3 m
(b)3√2/2 m
(c)6 m
(d)3√2 m
9.Write down the exact value of cos 45°.
(a)1/2
(b)√2/2
(c)√3/2
(d)√2
10.Write down the exact value of sin 0°.
(a)1/2
(b)0
(c)1
(d)undefined
11.Write down the exact value of sin 60°.
(a)1/2
(b)√2/2
(c)√3/2
(d)√3
12.Work out the exact value of sin 30° + cos 60°.
(a)0
(b)√3
(c)1
(d)1/2
13.A cable supporting a flagpole is anchored to the ground 5 m from the base of the pole. The cable makes an angle of 60° with the ground. Using the exact value of tan 60°, work out the exact height of the flagpole.
(a)10√3 m
(b)5/√3 m
(c)5√3 m
(d)5√3/2 m
14.A right-angled triangle has a hypotenuse of 10 cm. One of its other angles is 45°. Work out the exact length of one of the two shorter sides.
(a)5√2 cm
(b)5√3 cm
(c)10√2 cm
(d)5 cm
15.Each of these has an exact value. Write down the one whose value is the greatest.
(a)cos 60°
(b)sin 45°
(c)tan 45°
(d)cos 30°

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