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Trigonometric Graphs & Equations (Cambridge (CIE) IGCSE Maths)

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  • What is the graph of y equals sin x for negative 360 degree less or equal than x less or equal than 360 degree?

    The graph of y equals sin x for negative 360 degree less or equal than x less or equal than 360 degree is:

    Graph of y = sin x.

  • What is the graph of y equals cos x for negative 360 degree less or equal than x less or equal than 360 degree?

    The graph of y equals cos x for negative 360 degree less or equal than x less or equal than 360 degree is:

    Graph of y = cos x.

  • What is the graph of y equals tan x for negative 360 degree less or equal than x less or equal than 360 degree?

    The graph of y equals tan x for negative 360 degree less or equal than x less or equal than 360 degree is:

    Graph of y = tan x.

  • True or False?

    The point open parentheses 0 comma space 0 close parentheses lies on the graph y equals sin x.

    True.

    The point open parentheses 0 comma space 0 close parentheses lies on the graph y equals sin x.

  • What is the y-intercept of the graph y equals cos x?

    The y-intercept of the graph y equals cos x is open parentheses 0 comma space 1 close parentheses.

  • What is the minimum y value of the graph y equals sin x?

    The minimum y value of the graph y equals sin x is -1.

  • True or False?

    The graph y equals cos x repeats itself every 180°.

    False.

    The graph y equals cos x does not repeat itself every 180°.

    It repeats itself every 360°.

  • True or False?

    The graph y equals tan x repeats itself every 180°.

    True.

    The graph y equals tan x repeats itself every 180°.

  • The graph y equals sin x repeats itself every how many degrees?

    The graph y equals sin x repeats itself every 360°.

  • True or False?

    The maximum y value on the graph y equals tan x is 1.

    False.

    The maximum y value on the graph y equals tan x is not 1.

    The graph y equals tan x does not have a maximum value.

  • How would you use a graph of y equals sin x to find the solutions of sin x equals 0.5 for 0 degree less or equal than x less or equal than 360 degree?

    To find the solutions of sin x equals 0.5 for 0 degree less or equal than x less or equal than 360 degree using the graph y equals sin x:

    • calculate one solution using inverse trig x equals sin to the power of negative 1 end exponent open parentheses 0.5 close parentheses

    • draw the horizontal line y equals 0.5

    • use the symmetry of the graph to find the other solution

    Graph of y = sin x. A vertical line at 30º on the x-axis meets the curve at y = 0.5. A horizontal line is drawn across from this point until it touches the curve again and a vertical line is drawn down from here until it meets the x-axis at 150º.

  • True or False?

    After finding the first solution for an equation involving the cosine function, you can find another solution by subtracting the first solution from 180º.

    False.

    After finding the first solution for an equation involving the cosine function, you can find another solution by subtracting the first solution from 360º.

    The cosine graph showing that to find a second solution to an equation involving cos can be done by subtracting the first solution from 360º.

  • What angle should you add to or subtract from a first solution to find another solution for an equation involving the tangent function?

    If you know a first solution for an equation involving the tangent function, you can add to or subtract 180º from it to find another solution .

    The graph y = tan x showing that you can add 180º to find another solution from a first solution.
Previous:3D Pythagoras & TrigonometryNext:Vectors

    1. Topic 1

      Number Toolkit

    2. Topic 2

      Set Notation & Venn Diagrams

    3. Topic 3

      Prime Factors, HCF & LCM

    4. Topic 4

      Powers, Roots & Standard Form

    5. Topic 5

      Fractions Toolkit

    6. Topic 6

      Percentages Toolkit

    7. Topic 7

      Simple & Compound Interest, Growth & Decay

    8. Topic 8

      Surds

    9. Topic 9

      Working with FDP

    10. Topic 10

      Working with Ratios

    11. Topic 11

      Compound Measures (Speed, Density, Pressure)

    12. Topic 12

      Time, Currency & Conversions

    13. Topic 13

      Rounding, Estimation & Bounds

    14. Topic 14

      Using a Calculator

    1. Topic 1

      Algebra Toolkit

    2. Topic 2

      Algebraic Roots & Indices

    3. Topic 3

      Expanding & Factorising Brackets

    4. Topic 4

      Linear Equations & Inequalities

    5. Topic 5

      Quadratic Equations

    6. Topic 6

      Rearranging Formulas

    7. Topic 7

      Simultaneous Equations

    8. Topic 8

      Algebraic Fractions

    9. Topic 9

      Forming & Solving Equations

    10. Topic 10

      Functions

    11. Topic 11

      Sequences

    12. Topic 12

      Proportion

    1. Topic 1

      Coordinate Geometry

    2. Topic 2

      Linear Graphs

    3. Topic 3

      Quadratic Graphs

    4. Topic 4

      Further Graphs & Tangents

    5. Topic 5

      Solving & Graphing Inequalities

    6. Topic 6

      Real-Life Graphs

    7. Topic 7

      Differentiation

    1. Topic 1

      Geometry Toolkit

    2. Topic 2

      Angles in Polygons & Parallel Lines

    3. Topic 3

      Bearings, Constructions & Scale Drawings

    4. Topic 4

      Circle Theorems

    1. Topic 1

      Area & Perimeter

    2. Topic 2

      Circles, Arcs & Sectors

    3. Topic 3

      Volume & Surface Area

    4. Topic 4

      Congruence & Similarity

    1. Topic 1

      Right-Angled Triangles (Pythagoras & Trigonometry)

    2. Topic 2

      Sine, Cosine Rule & Area of Triangles

    3. Topic 3

      3D Pythagoras & Trigonometry

    4. Topic 4

      Trigonometric Graphs & Equations

    1. Topic 1

      Vectors

    2. Topic 2

      Transformations

    1. Topic 1

      Basic Probability

    2. Topic 2

      Probability Diagrams (Tree & Venn Diagrams)

    3. Topic 3

      Conditional Probability

    1. Topic 1

      Averages & Range

    2. Topic 2

      Statistical Diagrams

    3. Topic 3

      Histograms

    4. Topic 4

      Cumulative Frequency

    5. Topic 5

      Scatter Graphs & Correlation