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Exact trig values

Exact trig values

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Right-angled triangle with angle theta and sides labelled opposite, adjacent, and hypotenuse In a right-angled triangle, the hypotenuse is opposite the right angle. Relative to the chosen angle θ\thetaθ, the other sides are called opposite and adjacent.

SOHCAHTOA tells you that sin⁡θ=oppositehypotenuse\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}sinθ=hypotenuseopposite​, cos⁡θ=adjacenthypotenuse\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}cosθ=hypotenuseadjacent​ and tan⁡θ=oppositeadjacent\tan\theta=\frac{\text{opposite}}{\text{adjacent}}tanθ=adjacentopposite​. In triangle questions, label the sides first and then choose the ratio.

An exact value is written with no rounding. So sin⁡(45∘)=22\sin(45^\circ)=\frac{\sqrt{2}}{2}sin(45∘)=22​​ is exact, while 0.7070.7070.707 is only an approximation.

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Practice questions

Question 1

1 mark

Write down the exact value of sin⁡(45)\sin(45)sin(45)

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What defines an exact value in trigonometry?

Exact trig values Revision Guide

  1. GCSE
  2. /Maths
  3. /Exact trig values

Revision notes for WJEC GCSE Maths Exact trig values: explanations and worked examples.

Practise questions

1 of 5

What is the exact value of cos⁡(90∘)+tan⁡(45∘)\cos(90^\circ)+\tan(45^\circ)cos(90∘)+tan(45∘)?