smc-978-20-Area of Sector

Trigonometry, 2ADV T1 EQ-Bank 4

The circle below has centre , radius and arc length .

The ratio of the radius to the length of the arc is .

Show that the area of the sector is . (2 marks)

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Trigonometry, 2ADV T1 2021 HSC 12

A right-angled triangle is cut out from a semicircle with centre . The length of the diameter is 16 cm and = 30°, as shown on the diagram.

Find the length of in centimetres, correct to two decimal places. (2 marks)

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Hence, find the area of the shaded region in square centimetres, correct to one decimal place. (3 marks)

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a.

b.

Trigonometry, 2ADV T1 SM-Bank 1 MC

A windscreen wiper blade can clean a large area of windscreen glass, as shown by the shaded area in the diagram below.

The windscreen wiper blade is 30 cm long and it is attached to a 9 cm long arm.

The arm and blade move back and forth in a circular arc with an angle of 110° at the centre.

The area cleaned by this blade, in square centimetres, is closest to

786
1382
2573
4524

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	$²$

Trigonometry, 2ADV T1 2016 HSC 7 MC

The circle centred at has radius 5. Arc has length 7 as shown in the diagram.

What is the area of the shaded sector

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$²$

Trigonometry, 2ADV T1 2004 HSC 4a

is a sector of a circle, centre and radius 6 cm.

The length of the arc is cm.

Calculate the exact area of the sector . (2 marks)

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$²$

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$²$

Trigonometry, 2ADV T1 2005 HSC 4a

A pendulum is 90 cm long and swings through an angle of 0.6 radians. The extreme positions of the pendulum are indicated by the points and in the diagram.

Find the length of the arc . (1 mark)

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Find the straight-line distance between the extreme positions of the pendulum. (2 marks)

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Find the area of the sector swept out by the pendulum. (1 mark)

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$²$

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i.

ii.

iii.

$²$

Trigonometry, 2ADV T1 2008 HSC 7b

The diagram shows a sector with radius and angle where .

The arc length is .

Show that . (2 marks)

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Calculate the area of the sector when . (2 marks)

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$²$

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ii.

		$²$

Trigonometry, 2ADV T1 2009 HSC 5c

The diagram shows a circle with centre and radius 2 centimetres. The points and lie on the circumference of the circle and .

There are two possible values of for which the area of is square centimetres. One value is .

Find the other value. (2 marks)

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Suppose that .

(1) Find the area of sector (1 mark)

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(2) Find the exact length of the perimeter of the minor segment bounded by the chord and the arc . (2 marks)

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(1) $²$
(2)

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i.

ii. (1)


		$²$

ii. (2)

Trigonometry, 2ADV T1 2013 HSC 13c

The region is a sector of a circle with radius 30 cm, centred at . The angle of the sector is . The arc lies on a circle also centred at , as shown in the diagram.

The arc divides the sector into two regions of equal area.

Find the exact length of the interval . (2 marks)

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MARKER’S COMMENT: Simply finding the area of sector

achieved half marks in this challenging question! Show your working.