Trig equation solving

Solving Trig Equations for Theta

Before we begin

I want to practice a few problems when the angle is on the unit circle before doing problems that are not. The next two slides are just that (and not on your paper)

Dropdown

If sinΘ=1/2, what does theta equal? There are two answers, put the smaller answer first

Select answer

and ​

Select answer

Dropdown

If cosΘ = -1/2, what does theta equal? There are two answers, put the smaller answer first

Select answer

and ​

Select answer

Reminder of steps

To find an angle when it is not on the unit circle you must follow these steps:
1. Rewrite (if necessary) into sines and cosines. ( this is needed only for sec and csc)
2. Identify your quadrants your answer will be in based on x and y values
3. Inverse trig function to isolate theta
4. Draw angle and Adjust values according to where it should lie for the Quadrants

Looking at this problem, we will need to rewrite because it is csc and we need either sine or cosine

​

2nd sheet, back, bottom left problem

Multiple Choice

Looking at it, looks like csc is rewritten to be sine.

So! I must ask, is sine associated with y or x?

• y

• x

Multiple Select

If sine is why so we are trying to figure out where y is negative, what two quadrants will our answers fall in?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

We need to isolate theta now and to do that, we must take the inverse of sine on both sides of our equations. Using a calculator you get that theta is -54.068 (roughly)

Math Response

Well if I draw -54.068 degree I am in Quadrant 4, which is where I need to be but the value is not between 0-360 like i need. What could I add to this value to find a COTERMINAL angle?

Type answer here

Correct Answer: 360

Deg^°

Rad

Multiple Choice

The reference angle will be the same for both angles in the two quadrants. I need my other angle to be in quadrant 3 so when I draw that it looks like this.

For me to get a value in quadrant three, what should I do with that 54.068 reference angle?

• add 360

• subtract from 360

• add to 180

• subtract from 180

So with adding 360 and and 54.068 to 180 you get the two answers to the side of 305.932 and 234.068

lets try one more problem step by step to see if you got it

Multiple Choice

Do we need to rewrite this equation?

• Yes

• No

Multiple Choice

is cosine related to x values or y values?

• x

• y

Multiple Select

What quadrants will my answers be in if x = -0.482

• 1

• 2

• 3

• 4

Math Response

Since it is in Quadrant 2, to get the other answer, we need a reference angle. use the image to help you find the green theta

remember 3 decimal places

Type answer here

Correct Answer: 61.184

Deg^°

Rad

Math Response

Use the image to help you find the last angle you need in quadrant 3.

Type answer here

Correct Answer: 241.184

Deg^°

Rad

in conclusion

Figured I should keep it simple since 1, I am not here for you today and 2 it can take a bit step by step like this

tomorrow we will also go over a quick question version and try some together in class.