- Trigonometric equations review
- Solving Trigonometric Equations
- How do you solve #sin(theta)= 0.4# over the interval 0 to 2pi?
Trigonometric equations review
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It is important to distinguish between an algebraic expression and an equation. An equation is a statement that two algebraic expressions are equal. It may be true or false, depending on the values of any variables involved. Here are some examples of equations. You probably remember a number of algebraic techniques for solving equations of different types. Another useful equation-solving method uses graphs.
Solving Trigonometric Equations
How do you solve #sin(theta)= 0.4# over the interval 0 to 2pi?
Solving trig equations is just finding the solutions of equations like we did with linear, quadratic, and radical equations, but using trig functions instead. Note that we will use Trigonometric Identities to solve trig problems in the Trigonometric Identity section. Important Note: There is a subtle distinction between finding inverse trig functions and solving for trig functions. We will learn how to do this here. Also note that sometimes we have to divide a sin by a cos to get a tan , as in one of the examples. And the last problem involves solving a trig inequality. Here are examples; find the general solution, or all real solutions for the following equations.
This circle has the centre at the origin and a radius of 1 unit. The point P can move around the circumference of the circle. At point P the -coordinate is and the -coordinate is. The values of and also change. The graphs of and can be plotted. The graph of has a maximum value of 1 and a minimum value of As the point P moves anticlockwise round the circle, the values of and change, therefore the value of will change.
Measurement and Geometry : Module 25 Year : PDF Version of module. In the module, Further Trigonometry , we saw how to use points on the unit circle to extend the definition of the trigonometric ratios to include obtuse angles. The sine, cosine and tangent of negative angles can be defined as well. In this module, we will deal only with the graphs of the first two functions.