Sine, Cosine, and Tangent Ratios (Leaving Cert Mathematics): Quizzes

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Sine, Cosine, and Tangent Ratios
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What do trigonometric ratios compare in a right-angled triangle?

Sides and angles

Which side is the hypotenuse in a right-angled triangle?

Longest side opposite the right angle

What is the definition of sin⁡A\sin A in a right-angled triangle?

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

What is the definition of cos⁡A\cos A in a right-angled triangle?

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

What is the definition of tan⁡A\tan A in a right-angled triangle?

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

In SOHCAHTOA, what does 'SOH' stand for?

Sine = Opposite over Hypotenuse

In SOHCAHTOA, what does 'TOA' stand for?

Tangent = Opposite over Adjacent

Which is a common Pythagorean triple mentioned in the note?

3-4-5

What is the fundamental trigonometric identity?

sin⁡2A+cos⁡2A=1\sin^2 A + \cos^2 A = 1

For which angles is the identity sin⁡2A+cos⁡2A=1\sin^2 A + \cos^2 A = 1 true?

Any angle

If sin⁡A=35\sin A = \frac{3}{5}, what is cos⁡2A\cos^2 A using the fundamental identity?

1625\frac{16}{25}

In SOHCAHTOA, what does 'CAH' stand for?

Cosine = Adjacent over Hypotenuse

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