Trigonometry Solved Problems Trigonometric Equations
Remember that the techniques we use for solving are not the same as those for verifying identities.
The basic rules of algebra apply here, as opposed to rewriting one side of the identity to match the other side.
When we want to calculate the function for an angle larger than a full rotation of 360° (2 We can also find missing side lengths.
The general rule is: When we know any 3 of the sides or angles we can find the other 3 (except for the three angles case) See Solving Triangles for more details.
The period of both the sine function and the cosine function is There are similar rules for indicating all possible solutions for the other trigonometric functions.
For any angle "θ": (Sine, Cosine and Tangent are often abbreviated to Get a calculator, type in "45", then the "sin" key: sin(45°) = 0.7071... Here we see the sine function being made by the unit circle: Note: you can see the nice graphs made by sine, cosine and tangent. Here are some examples: Because the angle is rotating around and around the circle the Sine, Cosine and Tangent functions repeat once every full rotation (see Amplitude, Period, Phase Shift and Frequency).Identities are true for all values in the domain of the variable.In this section, we begin our study of trigonometric equations to study real-world scenarios such as the finding the dimensions of the pyramids.Often we will solve a trigonometric equation over a specified interval.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.We can verify the solutions on the unit circle in [link] as well.While algebra can be used to solve a number of trigonometric equations, we can also use the fundamental identities because they make solving equations simpler.Trigonometry helps us find angles and distances, and is used a lot in science, engineering, video games, and more!The triangle of most interest is the right-angled triangle.We read the equation from left to right, horizontally, like a sentence.We look for known patterns, factor, find common denominators, and substitute certain expressions with a variable to make solving a more straightforward process.