Three Important Angles (Leaving Cert Mathematics): Quizzes

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Three Important Angles
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Which three angles are considered special in trigonometry for having exact values?

30°30°, 45°45°, 60°60°

What type of triangle produces the 45°45° angle for exact trigonometric ratios?

Isosceles right triangle

In an isosceles right triangle with sides of 1 unit, what is the length of the hypotenuse?

2\sqrt{2}

What is the exact value of sin⁡45°\sin 45°?

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

What is the exact value of tan⁡45°\tan 45°?

11

Which statement is true about sin⁡45°\sin 45° and cos⁡45°\cos 45°?

They are equal

What is the side ratio in a 30-60-90 triangle?

1:3:21:\sqrt{3}:2

What is the exact value of sin⁡60°\sin 60°?

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

What is the exact value of cos⁡60°\cos 60°?

12\frac{1}{2}

What is the exact value of tan⁡30°\tan 30°?

13\frac{1}{\sqrt{3}}

How are sin⁡30°\sin 30° and cos⁡60°\cos 60° related?

They are equal

What is the exact value of sin⁡230°+cos⁡245°\sin^2 30° + \cos^2 45°?

34\frac{3}{4}

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