3D Trigonometry (Edexcel GCSE Maths): Flashcards

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3D Trigonometry
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Rules used in 3D trigonometry vs 2D

Same fundamental rules as 2D

Main challenge in 3D trigonometry

Visualising problem & identifying triangles

3-step method for line-to-plane angles

Create right triangle → 2D sketch → Use trig

Step 1 of 3-step method for line-to-plane angles

Create a right-angled triangle

Step 2 of 3-step method for line-to-plane angles

Draw a 2D sketch and mark lengths

Step 3 of 3-step method for line-to-plane angles

Use appropriate trig ratio (sin, cos, or tan)

Pythagoras' theorem formula

a2+b2=c2a^2 + b^2 = c^2

Sine rule formula

asinA=bsinB=csinC\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

Cosine rule formula

a2=b2+c22bccosAa^2 = b^2 + c^2 - 2bc \cos A

Formula for sinθ\sin \theta using sides

oppositehypotenuse\frac{\text{opposite}}{\text{hypotenuse}}

Formula for cosθ\cos \theta using sides

adjacenthypotenuse\frac{\text{adjacent}}{\text{hypotenuse}}

Formula for tanθ\tan \theta using sides

oppositeadjacent\frac{\text{opposite}}{\text{adjacent}}

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