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  • Perplex
    IB Math AIHL
    /
    Trig equations & identities
    /

    Problems

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    Problem Bank - Trig equations & identities

    Access custom-built, exam-style problems for trig equations & identities. Each problem has a full solution and mark-scheme, as well as AI grading and support.

    Select a Difficulty:

    17 / 55 problems visible - Upgrade to view all problems

    IB: 5
    8

    0 / 5

    The circle below shows two sectors of equal area, QPR and TPR.

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    The sector PQR has perimeter 4.5 and the combined sector QPT has perimeter 5.5.

    1. Find the interior angle of sector QPR.

      [3]
    2. Hence or otherwise, find the area of the combined sector PQT.

      [2]
    9

    0 / 7

    The following diagram shows triangle PQR with PR =3, PQ =x and QR =2x, where x∈R.

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    It is given that sinQ^​=53​, where Q^​ is acute.

    Find the area of the triangle.

    [7]
    10

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    The circular sector AOB centered at O has radius R=9 and central angle AO^B=2π​. At the midpoint of the sector's first radius is the point M, and point C lies on the second radius of the sector.


    A semicircle centered at M with diameter 9 is drawn inside the circular sector. A second semicircle of radius r centered at C is drawn such that the two semicircles are tangent. The line segment MC passes through X, the point of tangency between the semicircles.

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    1. Show that [CB]=3.

      [3]
    2. Find the area of R1​.

      [5]
    3. Hence find R2​.

      [3]
    11

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    Solve the equation cos4x=sin2x for x∈[0,π]

    [7]
    12

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    Solve the equation 2sin2x+3cosx=3, 0≤x<2π.

    [6]
    13

    0 / 8

    Consider the function g(x)=asinbx+c for 0≤x≤24. The graph of g is shown in the diagram below.


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    The x-intercepts are q and r, and the point P lies at the minimum.

    1. Find the coordinates of P.

      [3]
    2. Find the value of q and the value of r.

      [5]
    14

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    16

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