Printable · GCSE Foundation · ages 14-16
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.
Exact trigonometric values worksheet — GCSE Foundation
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- 1.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.
- 2.Triangle DEF has a right angle at E. Angle DFE = 60° and EF = 9 cm. Work out the exact length of DE.
- 3.Write down the exact value of tan 45°.
- 4.Work out the exact value of (cos 45°)² + (sin 45°)².
- 5.Work out the exact value of sin 45° × cos 45°.
- 6.Work out the exact value of sin 30° + cos 60°.
- 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.
- 8.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.
- 9.Write down the exact value of cos 30°.
- 10.Write down the exact value of tan 0°.
- 11.Three of these are rational numbers and one is irrational. Write down the one that is irrational.
- 12.Work out the exact value of (sin 30°)² + (cos 30°)².
- 13.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.
- 14.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.
- 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.
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