FOUR

4.4 Trigonometric Equations of Quadratic Type = Solving Conditional Trigonometric Equations =



==To find the inverse cos(1/2) you want to find the angle whose cosine is 1/2, since there are two answers and you want to find the angle in quad. 1 when positive, and quad. 2 when negative and 1/2 in this case is positive, the answer in quad. 1 would be 60 degrees.==

4.2 Basic Sine, Cosine, Tangent equations

 * Solving Cos(x), Sin(x) where a = 1, 0, or -1**


 * cos x = 1**

To solve this equation you must get x on one side by itself, so you have to get rid of the the cosine on the left. you can do this by taking the inverse cos (1). So now the equation you would be left with is: The cosine is 1 at 0 degrees, and that is the only answer. The equation would be:
 * x = inverse cos(1)**
 * x = 0+360k**

Sin x = 1 To solve this equation you need to get x on a side by itself, so you have to get rid of the sine on the left side. You can do this by taking the inverse sin(1). The equation you will be left with is: x = inverse sin(1) The sin is 1 at 90 degrees, and because it is quadrantal this is the only answer. The equation for this would be: x = 0+360k

To solve tangent:

tan x= 1 To solve this equation you need to get x on a side by itself. To get ride of the tan on the left side you wil take the inverse of tan(1). The equation you will be left with is: x=inverse tan(1) The tan is positve 1 in quadrants 1 and 3. Therefore there will be two answers. The answer equations for this problem will be: x= 45 + 360k x= 225 + 360k


 * 4.3 Multiple Angle Equations **

This section is very similar to section 4.2 except for a few minor details. You will find values of these angles but there will be a value next to your x in your equations.

// Finding solutions in degrees to sin(2x)=1/2

2x=30+360k or 2x=150+360k x=15+180k x=60+180k


 * Because sine is positive in both quadrants 1 and 2 you would write two equations. Then you will simply divide each equation by 2 on both sides to get x by itself. So your final answers will be x=15+360k and x=60+360k.

Finding solutions in degrees to cos(x/2)=1/2**

x/2=inverse cos(1/2)
 * You will solove for x/2 by using the inverse cosine function as you did when you found sin(2x)=1/2 which look like this:

x/2=60+360k or x/2=300+360k x=120+720k x=600+720k**


 * In this case instead of dividing by 2 to get x by itself you will multiply by 2 to get x by itself. Because cosine is positive in quadrants 1 and 4 you will have 2 equations. //