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Cambridge IGCSE Mathematics practice

exam practice - Identify, draw, and analyze the graphs of the following functions for angles between 0° and 360°: y = sin x, y = cos x, and y = tan x. Solve equations involving sin x, cos x, or tan x within the range of 0° to 360°, such as sin x = 2 or 2 cos x + 1 = 0. - Trigonometric functions

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Trigonometric functions

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Paper 2Core or Extended Mathematics2 marks

Solving trigonometric equations with no solutions

Description

Equation involving sine

Consider the equation sin x = 2 for x between 0° and 360°. The sine function ranges only between -1 and 1.

  1. a

    State Explain why the equation sin x = 2 has no solutions for x between 0° and 360°.

    Aim for approximately 2 distinct marking points.

    [2]

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  • Topic focus: Trigonometric functions.
  • Question style: structured_mathematics.
  • Reasoning demand: reasoning.
  • Check the operation, notation, units, and final answer form against the question before moving on.

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Paper 2 structured question: Trigonometric functions

Paper 2Core or Extended Mathematics3 marks

Description

Graph of y = cos x

Consider the graph of y = cos x for x between 0° and 360°. The graph starts at y = 1 when x = 0°, decreases to y = 0 at 90°, reaches y = -1 at 180°, returns to y = 0 at 270°, and back to y = 1 at 360°.

  1. a

    Calculate Find all values of x between 0° and 360° that satisfy the equation 2 cos x + 1 = 0.

    Aim for approximately 3 distinct marking points.

    [3]