Exact trig values
AQA GCSE Maths revision on Exact trig values. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
A student claims that since sin(30) = 0.5 and sin(60) = 0.866, sin(90) must be 1.233. Why is this reasoning flawed?
- A) The sine function is not linear
- B) The student used the wrong unit for the angle
- C) The sine function only goes up to 1
- D) The student added the numbers instead of multiplying them
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Answer: The sine function is not linear
Students often wrongly assume that because angles increase at a constant rate, the resulting sine values should also increase proportionally. In reality, the sine function follows a curve, meaning equal increments in degrees do not result in equal increments in the sine value. Recognising this non-linearity is fundamental to understanding trigonometric graphs.
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Question 2
Which geometric shape is the most effective tool for deriving the exact trigonometric values for 30 degrees and 60 degrees?
- A) Equilateral triangle
- B) Isosceles triangle
- C) Right-angled scalene triangle
- D) Regular pentagon
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Answer: Equilateral triangle
By taking an equilateral triangle with side lengths of 2 and cutting it in half, you create a right-angled triangle with angles of 30 and 60 degrees. This allows you to use Pythagoras' theorem to find the third side, providing the exact ratios needed for sine, cosine, and tangent. This geometric approach removes the need for relying on calculator approximations.
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Question 3
If cos(x) = sin(x), what is the value of tan(x)?
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Answer: 1
The definition of the tangent of an angle is tan(x) = sin(x) / cos(x). If the sine and cosine of an angle are equal, dividing one by the other will always result in 1. This relationship highlights how trigonometric identities are derived from their basic definitions.
Want to test yourself on the remaining cards for this topic?
13 more questions on Exact trig values — plus mistakes tracking and spaced repetition across the whole Maths spec.