Hong Kong
Stage 4 - Stage 5

# Graphical solution of trigonometric equations involving sine and cosine (radians)

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.