![]() To find \theta, use the inverse sine function. Recall the rule that gives the format for stating all possible solutions for a function where the period is 2\pi : If we need to find all possible solutions, then we must add 2\pi k, where k is an integer, to the initial solution. Sine and cosine can only ever get as big as one. And so, because this is as big as cosine ever gets. In other words, every 2\pi units, the y-values repeat. So, I wanna use cosine because cosine starts at a maximum and by starting at a maximum, I mean, think about it, for a cosine of zero, if you remember your trig functions, cosine of zero is equal to one. The period of both the sine function and the cosine function is 2\pi. Additionally, like rational equations, the domain of the function must be considered before we assume that any solution is valid. In other words, trigonometric equations may have an infinite number of solutions. However, just as often, we will be asked to find all possible solutions, and as trigonometric functions are periodic, solutions are repeated within each period. Often we will solve a trigonometric equation over a specified interval. Such a shifting is referred to as a horizontal shift. ![]() Similar in many ways to solving polynomial equations or rational equations, only specific values of the variable will be solutions, if there are solutions at all. The graphs of sine and cosine are the same when sine is shifted left by 90 or d radians. Trigonometric equations are, as the name implies, equations that involve trigonometric functions. The graph of a sinusoidal function has the same general shape as a sine or cosine function. The function cosx is even, so its graph is symmetric about the y -axis. The function sinx is odd, so its graph is symmetric about the origin. Solving Linear Trigonometric Equations in Sine and Cosine The basic sine and cosine functions have a period of 2. Solve trigonometric equations with multiple angles.Solve trigonometric equations using fundamental identities.Solve trigonometric equations that involve factoring.Solve trigonometric equations using a calculator.Solve equations involving a single trigonometric function.
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