 New Zealand
Level 8 - NCEA Level 3

Graphical solution of trigonometric equations involving sine and cosine

Lesson

Solutions to an equation exist at the points where the curve crosses the $x$x axis.

When we say find the solution to $y=f(x)$y=f(x), we are asking find all the values that make $f(x)=0$f(x)=0

Some functions have one solution; like linear, exponential and log functions some have $2$2 solutions like quadratics some have $3$3 solutions like cubics and some may have an infinite number of solutions like the cyclic functions we are currently studying. Some functions, however, have no solutions,

Like linear functions that are horizontal lines  These absolute value functions And also some cyclic functions.  Cyclic functions that have been vertically translated may not have any solutions as they do not cross the $x$x-axis at all. Solutions to a cyclic curve using a graph can be done by reading off the $x$x-intercepts (roots/solutions) from the graph within the required domain that suits the context or given requirements.

Outcomes

M8-2

Display and interpret the graphs of functions with the graphs of their inverse and/or reciprocal functions