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Trigonometry basics flash cards (SOHCAHTOA)

Flash cards on trigonometry basics: SOHCAHTOA, labelling triangles, exact values for 0°, 30°, 45°, 60° and 90°, the sine and cosine rules, triangle area and radians.

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The cards, front and back

  1. 1
    Front

    What does SOHCAHTOA stand for?

    Back

    Sin = Opposite ÷ Hypotenuse, Cos = Adjacent ÷ Hypotenuse, Tan = Opposite ÷ Adjacent. It applies to right-angled triangles.

  2. 2
    Front

    How do you label the sides of a right-angled triangle?

    Back

    The hypotenuse is the longest side, opposite the right angle. The opposite side is across from the angle you are using. The adjacent side is next to that angle and is not the hypotenuse.

  3. 3
    Front

    How do you choose which ratio to use?

    Back

    Label the sides, tick the two you know or need (one side you know and one you want), then pick the ratio that uses those two sides.

  4. 4
    Front

    How do you find a missing angle?

    Back

    Work out the ratio, then use the inverse function on your calculator, such as θ = sin⁻¹(opposite ÷ hypotenuse). Check the calculator is in degree mode.

  5. 5
    Front

    An angle is 30° and the hypotenuse is 10 cm. Find the opposite side.

    Back

    opposite = 10 × sin 30° = 10 × ½ = 5 cm.

  6. 6
    Front

    Exact values of sin, cos and tan at 0°

    Back

    sin 0° = 0, cos 0° = 1, tan 0° = 0.

  7. 7
    Front

    Exact values of sin, cos and tan at 30°

    Back

    sin 30° = ½, cos 30° = √3 ÷ 2, tan 30° = 1 ÷ √3 (which equals √3 ÷ 3).

  8. 8
    Front

    Exact values of sin, cos and tan at 45°

    Back

    sin 45° = √2 ÷ 2 (which equals 1 ÷ √2), cos 45° = √2 ÷ 2, tan 45° = 1.

  9. 9
    Front

    Exact values of sin, cos and tan at 60°

    Back

    sin 60° = √3 ÷ 2, cos 60° = ½, tan 60° = √3.

  10. 10
    Front

    Exact values of sin, cos and tan at 90°

    Back

    sin 90° = 1, cos 90° = 0, and tan 90° is undefined.

  11. 11
    Front

    Which two triangles give the exact values?

    Back

    Half of an equilateral triangle with side 2 (sides 1, √3 and 2) gives 30° and 60°. A right-angled isosceles triangle with shorter sides 1 (hypotenuse √2) gives 45°.

  12. 12
    Front

    What is the identity linking sin, cos and tan?

    Back

    tan θ = sin θ ÷ cos θ.

  13. 13
    Front

    What is the Pythagorean identity?

    Back

    sin²θ + cos²θ = 1, for any angle θ.

  14. 14
    Front

    The sine rule

    Back

    a ÷ sin A = b ÷ sin B = c ÷ sin C, where side a is opposite angle A, and so on. Use it when you know a side and its opposite angle.

  15. 15
    Front

    The cosine rule

    Back

    a² = b² + c² − 2bc cos A. Use it when you know two sides and the angle between them, or all three sides.

  16. 16
    Front

    Area of any triangle using trigonometry

    Back

    Area = ½ab sin C, where a and b are two sides and C is the angle between them.

  17. 17
    Front

    What are angles of elevation and depression?

    Back

    The angle of elevation is measured up from the horizontal to an object above. The angle of depression is measured down from the horizontal to an object below.

  18. 18
    Front

    What is a radian?

    Back

    The angle at the centre of a circle made by an arc equal in length to the radius. π radians = 180°, so 1 radian is about 57.3°.

  19. 19
    Front

    Convert 90° and 60° to radians.

    Back

    90° = π/2 radians. 60° = π/3 radians. Multiply degrees by π ÷ 180.

  20. 20
    Front

    What is the period of y = sin x and y = cos x?

    Back

    360° (2π radians). Both graphs repeat every full turn and stay between −1 and 1.

  21. 21
    Front

    What is the period of y = tan x?

    Back

    180° (π radians). The graph has vertical asymptotes at 90°, 270° and so on, where tan is undefined.

How to use this template

This deck covers the trigonometry you need before tackling harder problems: SOHCAHTOA, labelling a right-angled triangle, choosing the right ratio, finding sides and angles, the exact values for 0°, 30°, 45°, 60° and 90° and the triangles they come from, the two key identities, the sine and cosine rules, the area of a triangle, angles of elevation and depression, radians and the periods of the trig graphs. It suits GCSE and IGCSE maths (higher tier), Year 10 to Year 12 maths, high school geometry, precalculus and the start of A level, IB or AP courses. Learn the exact values until they are automatic using Test mode and spaced repetition, and print the deck double-sided for quick drills.

Tips

  • Draw the two special triangles from memory each time you revise. If you can draw them, you can work out every exact value.
  • Label hypotenuse, opposite and adjacent on every right-angled triangle before you choose a ratio.
  • Check that your calculator is in degrees for degree questions and radians for radian questions. Many wrong answers come from the wrong mode.
  • Notice the patterns: sin goes 0, ½, √2/2, √3/2, 1 from 0° to 90°, and cos goes the same way in reverse.
  • Only use the sine and cosine rules when the triangle is not right-angled. For right-angled triangles, SOHCAHTOA is quicker.

Make it fit

  • Turn on reverse cards so the value is on the front and you name the angle and ratio.
  • Add the unit circle, trig graphs and their transformations for an advanced course.
  • Remove the radians cards if your course has not reached them yet.
  • Add worked examples with bearings or 3D shapes from your own textbook.

Updated October 28, 2026

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