6.5 Solving trigonometric equations using pythagorean identities
Trigonometric equations are expressions comprised of the one or more of the trigonometric identities and a constant. An example of a trigonometric equation is $6sin^2\theta + 3 sin \theta = 0$. This equation is a second degree equation because the highest exponent is 2 and it is composed of the constant zero, and the coefficients 6 and 3.

In the previous chapters, we have learned about trigonometric ratios, functions identities and graph. By now, we already have a clear grasp of trigonometry. In this chapter, we will try to learn a bit more by applying all of the concepts we have learned to solve trigonometric equations.

In this chapter, we have seven parts that will cover everything that you have to understand about Trigonometric functions. In this chapter, we will review the Pythagorean theorem but instead of using a, b, and c, we will use x, y and 1. This will give us the equation, $x^2 + y^2$ = 1.

The equation above is used because we will use a unit circle all throughout the discussion. It will be very useful to review our discussion about the different angles like reference angles, co-terminal angles and standard angles to effectively understand this chapter.

In the first section, we will look at how to solve first-degree trigonometric equations like sin $\theta$, cos $\theta$ and tan $\theta$. In the exercises, we will look at how to solve for x in radian or in degree measure. In the second part of the chapter, we will look at the non-permissible value for trigonometric expression.

This discussion will be followed by the topic on how to solve second-degree trigonometric equations. As mentioned earlier, by definition, this kind of equation’s highest equation is 2, as in $sin^2\theta$ and $cos^2\theta$. We give you a step by step guide on how to do this.

In the next four chapters, we will solve trigonometric functions using multiple angles, Pythagorean identities, sum and difference identities and double-angle identities. We have studied about the different identities from the previous chapter, so it will also be best if you review all of these for this chapter.