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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 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
2.A ladder rests against a wall, making an angle of 60° with the ground. The ladder is 2 m long. Using the exact value of sin 60°, work out how high up the wall the ladder reaches, giving your answer in centimetres.
(a)200√3 cm
(b)√3 cm
(c)100√3 cm
(d)50√3 cm
3.Work out the exact value of sin 30° + cos 60°.
(a)0
(b)√3
(c)1
(d)1/2
4.Work out the exact value of (sin 30°)² + (cos 30°)².
(a)1/4
(b)3/4
(c)−1/2
(d)1
5.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
6.Write down the exact value of cos 45°.
(a)1/2
(b)√2/2
(c)√3/2
(d)√2
7.Work out the exact value of cos 0° − sin 30°.
(a)1/2
(b)−1/2
(c)3/2
(d)1
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 sin 45°.
(a)√3/2
(b)√2/2
(c)1/2
(d)1
10.Write down the exact value of sin 0°.
(a)1/2
(b)0
(c)1
(d)undefined
11.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
12.Here are four trigonometric ratios of special angles. Write down the one that does not have a value.
(a)sin 90°
(b)tan 90°
(c)tan 0°
(d)cos 90°
13.Write down the exact value of cos 30°.
(a)1
(b)1/2
(c)√2/2
(d)√3/2
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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