Interpreting the trigonometric graphs
I can read values from the graphs and can identify how many solutions exist within a given range.
- Year 11
Interpreting the trigonometric graphs
I can read values from the graphs and can identify how many solutions exist within a given range.
Lesson details
Key learning points
- Reading solutions from trigonometric graphs is the same as reading solutions from any other graph
- Due to the period, there may be more than one solution
- It is possible to predict the number of solutions that exist within a given range
Keywords
Trigonometric functions - Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle for a given angle.
Sine function - The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.
Cosine function - The cosine of an angle (cos(θ°)) is the x-coordinate of point P on the triangle formed inside the unit circle.
Tangent function - The tangent of an angle (tan(θ°)) is the y-coordinate of point Q on the triangle which extends from the unit circle.
Period (of a function) - For a repeating function, the period is the distance of one repetition of the entire function.
Common misconception
Pupils assume that the graph displayed always shows the number of solutions.
It is important to compare the range of values that the graph is displaying against what is being defined in the question.
Licence
Prior knowledge starter quiz
6 Questions
Q1.For a repeating function, the __________ is the distance of one repetition of the entire function.
Q2.Match the equivalent values.
$$\tan(20°)$$ - 0.364 (3 s.f)
$$\tan(80°)$$ - 5.67 (3 s.f)
$$\tan(97°)$$ - -8.14 (3 s.f)
$$\tan(105°)$$ - -3.73 (3 s.f)
Q3.Considering the cosine graph, what is the interval range showing a period?
Q4.Match the values of $$x$$ to the values of $$y$$ given $$y=x^2$$.
$$x = 5$$ - $$y = 25$$
$$x = 2$$ - $$y = 4$$
$$x = -3$$ - $$y = 9$$
$$x = 8$$ - $$y = 64$$
$$x = -6$$ - $$y = 36$$