Math AA SL: Trigonometry

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[Maximum Marks: 6]

The following diagram shows a triangle ABC.
The area of triangle ABC is 100 cm^2, AB=18 cm, AC=x and BAC=50°.

a. Find x.

b. Find BC. 

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[Maximum Mark: 7]

Find the value of x in 4\cos{x}=\sin{2x}
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[Maximum Mark: 7]

Find the value of x in \cos{2x}=\sin{x}^{2}+\cos{x}^{2}
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[Maximum Mark: 7]

Find the value of x in \sin(\frac{\pi}{2}-x)=\csc^{2}(x)-\cot^{2}(x)
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[Maximum Mark: 8]

Verify the trigonometric identity (\csc{x}+\cot{x})(\csc{x}-\cot{x})=1
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[Maximum Mark: 8]

Verify that \tan{x}+\cot{x}= \sec{x}\csc{x}
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Given that \sin(x)= {1/4}, where {x} is an acute angle, find the value of

a) \cos(x)

b) \cos(2x)
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Find CB

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[Maximum Mark: 7]

There is a circle O as shown below
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Angle O is 3.6 radians

a)Find the length of AB

b)Find the area of the shaded region
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