Trigonometric inequalities and choosing roots
Use a graph to see where a sine or cosine is above or below a number, and pick the roots of an equation on a given segment.
- Russia: grade 11
Guide
sin x > a is solved from the graph: where is the curve above the horizontal line y = a? The ends of the interval solve sin x = a.
With the period the answer is π/6 + 2πk < x < 5π/6 + 2πk, with k a whole number.
To choose roots, try whole k in x = π/4 + 2πk until the root lands on the segment. This is an advanced topic.