Trigonometric Exact Values: Sin, Cos and Tan — Interactive Lesson (Ages 14–16)

Do your students know where exact values come from? This 18-slide interactive lesson builds trigonometric exact values from two simple triangles, then extends them to angles up to 360°.

Learning Trigonometric Exact Values in Year 10–11 Maths

Students derive the exact values of sin, cos and tan for 45° from a right-angled isosceles triangle with a hypotenuse of √2, and for 30° and 60° from an equilateral triangle of side 2 cut in half. They then meet angles greater than 90°, learning which ratios are positive in each quadrant and how to write an angle in terms of θ, before applying the rules without a calculator to values such as cos 150° and tan 135°.

What’s Included

• 18-slide interactive lesson on exact values of sin, cos and tan
• Derivations from a right-angled isosceles triangle and an equilateral triangle
• The quadrant rules for angles between 0° and 360°
• Worked examples such as cos 150° and cos 330°
• No-calculator practice with self-marking questions

Key Benefits for Students

• Shows where the exact values come from, not just what they are
• Makes the quadrant rules clear and easy to apply
• Builds calculator-free confidence with trigonometry
• Instant feedback on answer questions

Why Teachers Love It

• No prep — ready for whole-class teaching on an interactive whiteboard
• Worked examples model how to set out each calculation
• Self-marking questions support independent practice
• Suits teaching, revision and homework
• A natural next step after basic trigonometry

Love this? You’ll love…

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A dependable addition to a GCSE trigonometry topic, giving students a clear reason behind each exact value rather than a list to memorise. Secure understanding here supports non-calculator papers and later work at A-Level.

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FAQ

What year group is this for? Years 10–11 (ages 14–16), GCSE.

Which angles are covered? Exact values for 30°, 45° and 60°, extended to angles up to 360° using the quadrant rules.

Is it self-marking? Yes, with instant feedback on the questions.