Exact Trig Values
Forget about memorising random numbers - exact trigonometric values follow brilliant patterns that make them dead easy to remember. You'll need these for your GCSE maths, and once you spot the tricks, you'll never forget them.
The magic happens with three special angles: 30ยฐ, 45ยฐ, and 60ยฐ. These come from two fundamental triangles - the 45-45-90 triangle (an isosceles right triangle) and the 30-60-90 triangle. Both triangles give you all the exact values you need.
Here's the genius part: sin values have numerators that go โ0, โ1, โ2, โ3, โ4 (from 0ยฐ to 90ยฐ), whilst cos values do the exact opposite - they decrease from โ4 to โ0. The denominator is always 2, except when it simplifies to 1 or 0.
For tan values, just remember that tan = sin รท cos. So tan(45ยฐ) = (โ2/2) รท (โ2/2) = 1. Simple as that! The pattern becomes: 0, 1/โ3, 1, โ3, and undefined for 90ยฐ.
Quick Tip: Draw the grid first, then simplify! Start with the square root pattern, then work out which fractions can be simplified.