Exact Trig Values (Edexcel GCSE Maths: Foundation)

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Exact Trig Values

What are the exact values in trigonometry?

  • Trigonometry could appear on the non-calculator paper
  • You will need to know the following exact values
theta equals 0 degree 30 degree 45 degree 60 degree 90 degree
sin theta equals 0 1 half fraction numerator square root of 2 over denominator 2 end fraction fraction numerator square root of 3 over denominator 2 end fraction 1
cos theta equals 1 fraction numerator square root of 3 over denominator 2 end fraction fraction numerator square root of 2 over denominator 2 end fraction 1 half 0
tan theta equals 0 fraction numerator square root of 3 over denominator 3 end fraction 1 square root of 3 Not Defined

 

  • Note that the values of sin θ  going from 0° to 90° match those of cos θ going from 90° to 0°

How are exact trig values for 30° and 60° derived?

  • Draw an equilateral triangle where the length of each side is 2
    • Each angle will be 60°
  • Halve the triangle to form a right-angled triangle where one of the lengths is now 1
    • One angle will now be 30°
  • Find the length of the missing side using Pythagoras
  • Use SOHCAHTOA to find the exact values of the trig ratios for 30° and 60°

Exact Values Notes Diagram 2

How are exact trig values for 45° derived?

  • Draw an isosceles right-angled triangle where the length of the equal sides is 1
    • The two equal angles will be 45°
  • Find the length of the missing side using Pythagoras
  • Use SOHCAHTOA to find the exact values of the trig ratios for 45°

5-4-2-exact-values-notes-diagram-1

Examiner Tip

  • If you forget the exact values in your exam
    • Use a value that you think it could be
    • Even if the value you used is incorrect, you will still get method marks for the rest of the question

Worked example

The following diagram is not drawn to scale.

exact-trig-values-we

Without using a calculator, find the value of x.

You have the hypotenuse and the side that is adjacent to the angle
Use CAH

cos open parentheses 60 close parentheses equals x over 24

Multiply both sides by 24

x equals 24 cross times cos open parentheses 60 close parentheses

Use cos open parentheses 60 close parentheses equals 1 half

x equals 24 cross times 1 half

bold italic x bold equals bold 12

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Dan

Author: Dan

Expertise: Maths

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.