Tooltip
These resources have been reviewed and selected by STEM Learning’s team of education specialists for factual accuracy and relevance to teaching STEM subjects in UK schools.

Finding All the Solutions of Trigonometric Equations

The mathematical solution explains how to solve the equation: sin(x+150) = 1/sqrt2 for x between 0⁰ and 360⁰. To begin with, the principle values for (x+150) are found. The fact that a sine curve is periodic is used to find the solution set for (x+150) based upon these two initial values. Subtracting 150 from each member of the solution set gives a solution set for x. From this solution set values for x in the required range can be identified.

Graphical solution 1 shows how a graphical calculator can be used to verify the solution. The first step is to use the calculator to draw the graph of y=sin(x+150) and the graph of y= 1/sqrt2. The graphical calculator is then used to find the points of intersection of the two graphs confirming the mathematical solutions.

Graphical solution 2 shows the mathematical solution to the equation cos(4x) = -1/2 and explains how the solutions found can be verified graphically by finding the points of intersection of the graphs y= cos(4x) and y= -1/2.

 

Show health and safety information

Please be aware that resources have been published on the website in the form that they were originally supplied. This means that procedures reflect general practice and standards applicable at the time resources were produced and cannot be assumed to be acceptable today. Website users are fully responsible for ensuring that any activity, including practical work, which they carry out is in accordance with current regulations related to health and safety and that an appropriate risk assessment has been carried out.

Information on the permitted use of this resource is covered by the Category Three Content section in STEM Learning’s Terms and conditions.

Lists that tag this content