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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.Work out the exact value of (cos 45°)² + (sin 45°)².
(a)2
(b)√2
(c)1
(d)1/2
2.Write down the exact value of tan 60°.
(a)1/√3
(b)3
(c)√3/2
(d)√3
3.Work out the exact value of sin 45° × cos 45°.
(a)√2
(b)1
(c)1/2
(d)√2/2
4.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
5.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
6.Write down the exact value of cos 30°.
(a)1
(b)1/2
(c)√2/2
(d)√3/2
7.Work out the exact value of tan 30° + tan 30°.
(a)2√3/3
(b)√3/3
(c)√3
(d)2√3
8.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°
9.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
10.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.
(a)12√3 cm
(b)6 cm
(c)4√3 cm
(d)6√3 cm
11.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
12.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
13.Work out the exact value of (sin 30°)² + (cos 30°)².
(a)1/4
(b)3/4
(c)−1/2
(d)1
14.Write down the exact value of sin 0°.
(a)1/2
(b)0
(c)1
(d)undefined
15.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

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