Trigonometry in two dimensions (AQA GCSE Further Maths): Flashcards

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Trigonometry in two dimensions
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Formula for sin⁡θ\sin \theta

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

Formula for cos⁡θ\cos \theta

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

Formula for tan⁡θ\tan \theta

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

SOH in SOHCAHTOA means

Sine = Opposite over Hypotenuse

CAH in SOHCAHTOA means

Cosine = Adjacent over Hypotenuse

TOA in SOHCAHTOA means

Tangent = Opposite over Adjacent

Which side is the hypotenuse?

Longest side, opposite the right angle

Use of inverse trig functions (sin⁡−1\sin^{-1}, cos⁡−1\cos^{-1}, tan⁡−1\tan^{-1})

Find angles when two sides are known

Angle of elevation measured from

Horizontal line upward

Angle of depression measured from

Horizontal line downward

Exact value of sin⁡30°\sin 30°

12\frac{1}{2}

Exact value of sin⁡45°\sin 45°

12\frac{1}{\sqrt{2}}

Exact value of tan⁡45°\tan 45°

11

Exact value of sin⁡60°\sin 60°

32\frac{\sqrt{3}}{2}

Exact value of tan⁡60°\tan 60°

3\sqrt{3}

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