8-1 Simple Trigonometric Eqns.

This past week in Advanced Math, we learned sections 8-1 through 8-3. We learned part I of 8-1 on Friday and part II on Wednesday. 8-1 is about solving simple trigonometric equations. We were taught how to solve simple trigonometric equations and also how to apply them. To solve an equation involving a trigonometric function, we first transform the equation so that the function is alone on one side of the equals sign.

To solve for theta, you get the trig function by itself then take an inverse. Remember, an inverse has two answers with some exceptions! Here are the steps to follow:
1. Take the inverse of the positive number to find the quadrant one angle.
2. For quadrant two, make it negative and add 180 degrees.
3. For quadrant three, just add 180 degrees.
4. And for quadrant four, make the number negative and add 360 degrees.

With that in mind, let’s try an example problem..
EXAMPLE 1: 3 sin theta = 2
A). First, transform the equation so that the function is alone on one side. Dividing 3 from the
left and right, you will then get sin theta = 2/3.
B). Now, take the inverse of 2/3 to find quadrant one’s angle – theta = sin ^-1(2/3)
C). Plugging that into your calculator, you will get 41.8 degrees. Now, draw your coordinate
plane and place 41.8 in quadrant one. We know that sine is positive in quadrants I and II, so solve for those angles.
D). For quadrant II, make 41.8 negative and add 180 degrees. You will get 138.2 degrees. That is your quadrant II angle.

EXAMPLE 2: 2 cos theta = 1
A). Like in example one, divide 2 from the left and right to get cos theta = ½.
B). Now, take the inverse of ½ to find quadrant one’s angle – theta = cos ^-1(1/2)
C). Plugging that into your calculator, you will get 60 degrees. Now, draw your coordinate plane and place 60 degrees in quadrant one. We know that cosine is positive in quadrants I and IV. Since we have quadrant one’s angle, solve for quadrant four’s by making 60 negative and adding 360 degrees. Your answer will be 300 degrees.


These are two examples from section 8-1, part I which we learned on Friday. Part II of 8-1 deals with inclinations and slopes but still requires solving trigonometric equations.