Sketch single standard trig graph (sin/cos/tan)

Sketch the graph of a single sin, cos, or tan function (possibly with amplitude/period/phase transformations) over a specified interval, where the function is NOT an inverse or reciprocal trig function.

10 questions · Moderate -1.0

Sort by: Default | Easiest first | Hardest first
CAIE P1 2017 June Q5
7 marks Moderate -0.8
5 The equation of a curve is \(y = 2 \cos x\).
  1. Sketch the graph of \(y = 2 \cos x\) for \(- \pi \leqslant x \leqslant \pi\), stating the coordinates of the point of intersection with the \(y\)-axis. Points \(P\) and \(Q\) lie on the curve and have \(x\)-coordinates of \(\frac { 1 } { 3 } \pi\) and \(\pi\) respectively.
  2. Find the length of \(P Q\) correct to 1 decimal place.
    The line through \(P\) and \(Q\) meets the \(x\)-axis at \(H ( h , 0 )\) and the \(y\)-axis at \(K ( 0 , k )\).
  3. Show that \(h = \frac { 5 } { 9 } \pi\) and find the value of \(k\).
Edexcel C2 Q4
10 marks Moderate -0.8
4. $$\mathrm { f } ( x ) = 5 \sin 3 x ^ { \circ } , \quad 0 \leq x \leq 180$$
  1. Sketch the graph of \(\mathrm { f } ( x )\), indicating the value of \(x\) at each point where the graph intersects the \(x\) axis.
  2. Write down the coordinates of all the maximum and minimum points of \(\mathrm { f } ( x )\).
  3. Calculate the values of \(x\) for which \(\mathrm { f } ( x ) = 2.5\) [0pt] [P1 June 2002 Question 5]
Edexcel C2 Q36
8 marks Moderate -0.8
  1. Sketch, for \(0 \leq x \leq 360°\), the graph of \(y = \sin (x + 30°)\). [2]
  2. Write down the coordinates of the points at which the graph meets the axes. [3]
  3. Solve, for \(0 \leq x < 360°\), the equation $$\sin (x + 30°) = -\frac{1}{2}.$$ [3]
Edexcel C2 Q4
8 marks Moderate -0.8
  1. Sketch, for \(0 \leq x \leq 360°\), the graph of \(y = \sin (x + 30°)\). [2]
  2. Write down the coordinates of the points at which the graph meets the axes. [3]
  3. Solve, for \(0 \leq x < 360°\), the equation $$\sin (x + 30°) = -\frac{1}{2}.$$ [3]
Edexcel C2 Q7
9 marks Moderate -0.8
The curve C has equation \(y = \cos \left(x + \frac{\pi}{4}\right)\), \(0 \leq x \leq 2\pi\).
  1. Sketch C. [2]
  2. Write down the exact coordinates of the points at which C meets the coordinate axes. [3]
  1. Solve, for x in the interval \(0 \leq x \leq 2\pi\), $$\cos \left(x + \frac{\pi}{4}\right) = 0.5,$$ giving your answers in terms of π. [4]
Edexcel C2 Q4
8 marks Moderate -0.8
  1. Sketch, for \(0 \leq x \leq 360°\), the graph of \(y = \sin (x + 30°)\). [2]
  2. Write down the coordinates of the points at which the graph meets the axes. [3]
  3. Solve, for \(0 \leq x < 360°\), the equation \(\sin (x + 30°) = -\frac{1}{2}\). [3]
Edexcel C2 Q3
9 marks Moderate -0.8
The curve \(C\) has equation \(y = \cos \left( x + \frac{\pi}{4} \right)\), \(0 \leq x \leq 2\pi\).
  1. Sketch \(C\). [2]
  2. Write down the exact coordinates of the points at which \(C\) meets the coordinate axes. [3]
  3. Solve, for \(x\) in the interval \(0 \leq x \leq 2\pi\), \(\cos \left( x + \frac{\pi}{4} \right) = 0.5\), giving your answers in terms of \(\pi\). [4]
OCR C2 Q6
8 marks Moderate -0.8
$$f(x) = \cos 2x, \quad 0 \leq x \leq \pi.$$
  1. Sketch the curve \(y = f(x)\). [2]
  2. Write down the coordinates of any points where the curve \(y = f(x)\) meets the coordinate axes. [3]
  3. Solve the equation \(f(x) = 0.5\), giving your answers in terms of \(\pi\). [3]
AQA Paper 3 2022 June Q5
3 marks Easy -1.2
  1. Sketch the graph of $$y = \sin 2x$$ for \(0° \leq x \leq 360°\) \includegraphics{figure_5a} [2 marks]
  2. The equation $$\sin 2x = A$$ has exactly two solutions for \(0° \leq x \leq 360°\) State the possible values of \(A\). [1 mark]
Pre-U Pre-U 9794/2 2012 June Q5
3 marks Easy -2.0
Sketch, on separate diagrams, the graphs of the following functions for \(0 \leqslant x \leqslant 2\pi\) giving the coordinates of all points of intersection with the axes.
  1. \(y = \sin x\). [1]
  2. \(y = \sin\left(x + \frac{1}{6}\pi\right)\). [2]