HAEF IB - MATH SL

TEST 6 – (Paper 1: Without GDC)

Trigonometry

by Christos Nikolaidis

Name:______

Date: 31 – 3 – 2016

Questions

1.  [Maximum mark: 8]

Given that sinA=0.6, where 90°≤A≤180°, find the following values in two decimal places.

(a)  cosA [3 marks]

(b)  tanA [2 marks]

(c)  cos2A [3 marks]

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2.  [Maximum mark: 8]

Solve the following equations. The solutions must be given in terms of π.

(a)  2sin2x-3sinx=-1, 0≤x≤3π [6 marks]

(b)  2cos2x+3sinx=3, 0≤x≤3π [2 marks]

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3.  [Maximum mark: 10]

Solve the following equations. The solutions must be given in terms of π.

(c)  sin2x=3cosx, -π≤x≤π [6 marks]

(d)  3sinx=cosx, 0≤x≤2π [4marks]

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4.  [Maximum mark: 7]

Let

A=cosx+sinx

B=cosx-sinx

(a)  Express A2 in the form asin2x+b [3 marks]

(b)  Express AB in form acosbx [2 marks]

(c)  Given that A2+B2=c, find the value of the integer c. [2 marks]

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5.  [Maximum mark: 12]

Consider the graph of the function fx=asin⁡(bx)+c

It has a maximum at A(1,14) and a minimum at B(3,4)

(a)  Write down the range of the function [1 mark]

(b)  Write down the y-intercept of the function [1 mark]

(c)  Find the period of the function [2 marks]

(d)  Find the values of a, b and c. [4 marks]

(e)  Express the function in the form fx=acos⁡(bx-d)+c,

(i)  given that a is positive. [2 marks]

(ii)  given that a is negative. [2 marks]

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Page 6

HAEF IB - MATH SL

TEST 6 – (Paper 2: With GDC)

Trigonometry

by Christos Nikolaidis

Name:______

Date: 31 – 3 – 2016

Questions

1.  [Maximum mark: 5]

Find the values of x in the following cases

(a) sinx=0.3, 0≤x≤3π (in radians) [2 marks]

(b) cosx=0.3, -180°≤x≤360° (in degrees) [3 marks]

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2.  [Maximum mark: 5]

In the triangle ABC, A = 30°, B =50° and AB = 5. Find the length of BC.

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3.  [Maximum mark: 6]

Consider the function

fx=sin2x-cos3x

(a)  By observing its graph in your GDC, find the range and the period of f [4 marks]

(b)  Solve the equation

sin2x=cos3x, 0≤x≤3π [2 marks]

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4.  [Maximum mark: 5]

Consider the following diagram.

[5 marks]

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5.  [Maximum mark: 9]

The diagram shows a circle of centre O and radius r=5. Let AOB = θ radians.

(a)  Given that θ is 120°, find

(i)  the length of the minor arc ACB, [2 marks]

(ii)  the area of the minor sector OACB [2 marks]

(iii)  the area of the shaded region [3 marks]

(b)  Find the value of θ , given that the area of the shaded region is 12. [2 marks]

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6.  [Maximum mark: 15]

Let ,

(a)  Sketch the graph of in the space below. Indicate the coordinates

of the y-intercept and of the maximum points.

[4 marks]

(b) Complete the following table for f.

Period / Range

[4 marks]

(b)  This function can be expressed in the form

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where are positive real numbers. Complete the following table for f.

a / b / c / d

[5 marks]

(c)  This function can also be expressed in the form

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where are as above. Find a possible value of d.

d

[2 marks]

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