Trigonometry worksheets
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Trigonometric ratios
Grade 9
Write sine, cosine and tangent as fractions of a right triangle's sides
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In teaching order
Trigonometry worksheets, easiest first
Each sheet assumes the one above it is comfortable. Start where your child is, not at the top.- Trigonometric ratios
Print 3-4-5 → sin A - Right-triangle trigonometry
Print 20, 65° → x - Radians and degrees
Print 90° → π/2 - Exact trig values
Print sin 30° → 1/2 - Pythagorean identity
Print sin A = 3/5 → cos A - Cofunctions of complementary angles
Print sin 40° → cos 50° - Law of sines
Print a, ∠A, ∠B → b - Law of cosines
Print a, b, ∠C → c - Area of a triangle with sine
Print a, b, ∠C → area - The six trig ratios
Print 3-4-5 → csc A - Finding a missing side
Print 12, 35° → side - Finding a missing angle
Print 9, 12 → angle
A simple way through trigonometry
It begins with the definition, before any calculator. A trig ratio is a fraction of a right triangle's sides — sin A is the opposite over the hypotenuse, read straight off the figure — and because every triangle here is a Pythagorean triple, the ratio stays an exact fraction. That is the ground the rest stands on: once the ratio is a known thing, solving a right triangle uses it to find a missing side or angle.
Why this order works
The unit circle is the year's memory work. Degrees and radians relate by one fact — a straight angle is 180° and also π radians — so every conversion is a single multiplication, with the answer left in terms of π. The exact values at the special angles come off two triangles, kept as surds rather than rounded, because a decimal hides the √3/2 a student is meant to recognise. The identities that follow, sin²+cos²=1 and the cofunction rule, tie the ratios of an angle together.