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Trigonometry GCSE questions

4th August 2022

Sin, cos, tan – these three abbreviations don’t need to strike fear in the hearts of students! With enough practice, the trig section of the maths GCSE can be a breeze. For help with this and other tough topics, try professional GCSE maths tuition with TLC LIVE.

In each one-to-one session, our tutors draw from an extensive library of targeted teaching resources. Here is a set of NUM example trigonometry GCSE questions from our library.

10 sample trigonometry GCSE questions

1. Trigonometry GCSE question: Find x to one d.p. The image shows a right-triangle with the hypotenuse labelled x. One side is labelled 25cm and the angle between them is 30 degrees.

2.A trigonometry GCSE question: Find x to one d.p. The image shows a right triangle with a hypotenuse of 23cm and a vertical of 12. The angle x is opposite the vertical.

3. a trigonometry GCSE question: Find x to one d.p. An image of a right triangle with the vertical labelled x. The hypotenuse is 17cm and the angle between the hypotenuse and the horizontal is 32 degrees.

4. a trigonometry GCSE question: Use the information below to find the value of Cos 50 degrees. Answer to 2 d.p. Do not use a calculator. Two right triangles are shown. The first has a hypotenuse of 1cm, an angle between the horizontal and the hypotenuse of 50 degrees, and a base of 0.64cm. The second also has a hypotenuse of 1cm and the angle between the horizontal and the hypotenuse of 50 degrees. The vertical is 0.77m.

5. a trigonometry GCSE question: Find the length of BC, answer in the form "A square root B" where A and B are integers. The triangle has a vertical of 6cm with B at the base of the vertical line and A at the top. C is at the connection between the hypotenuse and the horizontal, and shows 60 degrees.

6. a trigonometry GCSE question: Find the value of Sin 40 using the information below. Answer to 2 d.p. Do not use a calculator. Three triangles are shown. The first has a vertical of 0.77, a hypotenuse of 1, and an angle between the hypotenuse and the vertical of 40 degrees. The second has a base of 0.64, a hypotenuse of 1, and an angle between the hypotenuse and the vertical of 40 degrees. The third has a vertical of 1, a base of 0.84, and an angle between the hypotenuse and the vertical of 40 degrees.

7. a trigonometry GCSE question: Find the length of np. Answer to 1 d.p. Two vertical lines are shown. Mn is 1.9cm. Op is longer, but unlabelled. Below, text explains that mn : op = 1 :2.5 and that the angle of elevation of o from m is 43 degrees.

8.TLC trig 8

9. A trigonometry GCSE question: Find the area of the square, answer to 1 d.p. The image shows a square within a circle, where all of the square's corners are exactly touching the perimeter of the circle. The text explains that the circle's area is 50cm^2.

10. a trigonometry GCSE question: The square-based pyramid below has a height of 8cm. The sides of the square base all measure 4cm. X is at the midpoint of the square. Find angle y. A diagram is below. It shows the four corners of the base labelled A, B, C and D and the top labelled E. A point, x, is at the centre of the square. The angle y is between the lines AE and Ax.

Answers to our sample trigonometry GCSE questions

1. 9cm
2. 4
3. 9cm
4. 64
5. 2√3
6. 64
7. 76⁰
8. 1cm
9. 8cm²
10. 5⁰

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Written by Ryan Lockett, director of studies at TLC LIVE.