Solving Trig Equations

Finding solutions for sin(x) = 1/2

Utilize a unit circle or a graph

Expressing infinite solutions for an equation involving trig ratios

Adding the period (eg 2pi) multiplied by k (which represents an integer or the number of cycles passed) to the solution(s)

Goal in Solving Trigonometric Equations

Isolating the variable then finding values that satisfy the equation

Given a trigonometric equation with the default period, how many cycles does it run through given 0 < x < 4pi?

Two cycles

0 < x < 4pi versus -2pi < x < 2i, given a default period

Both go through two cycles, but the second includes a negative value, and therefore has one cycle on the negative x-axis

what is cos²(x) equivalent to?

cos(x) * cos(x)

Strategy in handling trigratio(x)’s

You can substitute trigratio(x) with a simple letter variable to make it easier to comprehend and solve