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HL TRIGONOMETRY

Quiz by Chris Kennedy

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Q 1/10
Score 0
A sector of a circle with radius r cmr cm​, where r>0r > 0​, is shown on the following diagram. The sector has an angle of 1 radian at the centre. Let the area of the sector be A cm2A cm^2​ and the perimeter be P cmP cm​. Given that A=PA=P​, find the value of rr​.
300
​r=7r=7​
​r=6r=6​
​r=5r=5​
​r=4r=4​

10 questions

Q.A sector of a circle with radius r cmr cm, where r>0r > 0, is shown on the following diagram. The sector has an angle of 1 radian at the centre. Let the area of the sector be A cm2A cm^2 and the perimeter be P cmP cm. Given that A=PA=P, find the value of rr.
1
300 sec
Q.Consider the following diagram. The sides of the equilateral triangle ABCABC have lengths 1 m1 m. The midpoint of [AB][AB] is denoted by PP. The circular arc ABAB has centre, MM, the midpoint of [CP][CP]. Find AMAM.
2
300 sec
Q.Consider the following diagram. The sides of the equilateral triangle ABCABC have lengths 1 m1 m. The midpoint of [AB][AB] is denoted by PP. The circular arc ABAB has centre, MM, the midpoint of [CP][CP]. Find angle AMPAMP in radians.
3
300 sec
Q.Consider the following diagram. The sides of the equilateral triangle ABCABC have lengths 1 m1 m. The midpoint of [AB][AB] is denoted by PP. The circular arc ABAB has centre, MM, the midpoint of [CP][CP]. Find the area of the shaded region.
4
300 sec
Q.This diagram shows a metallic pendant made out of four equal sectors of a larger circle of radius OB=9cmOB=9 cm and four equal sectors of a smaller circle of radius OA=3cmOA=3 cm. The angle BOC=20°BOC= 20°. Find the area of the pendant.
5
300 sec
Q.Given ΔABCΔABC, with lengths shown in the diagram below, find the length of the line segment [CD][CD].
6
300 sec
Q.The triangle ABCABC is shown in the following diagram. Given that cosB<14cosB<\frac{1}{4}, find the range of possible values for ABAB.
7
300 sec
Q.In a triangle ABCABC, AB=4cmAB=4 cm, BC=3cmBC=3 cm and angle BAC=π9BAC=\frac{π}{9}. Use the cosine rule to find the two possible values for ACAC.
8
300 sec
Q.In a triangle ABCABC, AB=4cmAB=4 cm, BC=3cmBC=3 cm and angle BAC=π9BAC=\frac{π}{9}. Use the cosine rule to find the two possible values for ACAC, then find the difference between the areas of the two possible triangles ABC.
9
300 sec
Q.In triangle ABCABC, AB=9cmAB = 9 cm, AC=12cmAC = 12 cm, and angle BB is twice the size of angle CC . Find the cosine of angle CC.
10
300 sec

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