smc-980-20-Trig Ratios

Trigonometry, 2ADV T1 2023 HSC 16

The diagram shows a shape . The shape consists of a rectangle with an arc on side and with side lengths = 3.6 m and = 8.0 m.

The arc is an arc of a circle with centre and radius 2.1 m and .

What is the perimeter of the shape ? Give your answer correct to one decimal place. (4 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 2016 HSC 1 MC

For the angle and

Which diagram best shows the angle

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Trigonometry, 2ADV T1 2007 HSC 4c

An advertising logo is formed from two circles, which intersect as shown in the diagram.

The circles intersect at and and have centres at and .

The radius of the circle centred at is 1 metre and the radius of the circle centred at is metres. The length of is 2 metres.

Use Pythagoras’ theorem to show that . (1 mark)

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Find and . (2 marks)

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Find the area of the quadrilateral . (1 mark)

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

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Find the total area of the logo (the sum of all the shaded areas). (2 marks)

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$²$
$²$
$²$

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ii.

iii.

$²$

iv.

$²$

$²$

Trigonometry, 2ADV T1 2005 HSC 9b

The triangle has a right angle at and . The line is drawn perpendicular to . The line is then drawn perpendicular to . This process continues indefinitely as shown in the diagram.

Find the length of the interval , and hence show that the length of the interval is . (2 marks)

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Show that the limiting sum

is given by . (3 marks)

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ii.

Trigonometry, 2ADV T1 2013 HSC 2 MC

The diagram shows the line .

What is the slope of the line ?

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