Math Help - Trigonometry questions involving multiple topics

Math is definitely NOT my subject & my "teacher" CAN'T teach. So some help would be amazing! Here are some example questions I want to understand:

1. How do you find the reference angles for:
-190°
-3π/4
5π/8

2. Are the following true or false & why?

cos(-175°) = cos(175°)
cos(32°) = sin(58°)
sin(π/3) = 1/sec(π/3)
cos(2π/3) = cos(4π/3)

3. Given sinθ = -3/4 and θ is in quadrant 4, find the following:

cosθ
tanθ
sin (-θ)
cos (-θ)

4. Given the function, f(x) = 2cos(x/2)+3

find the amplitude of f(x)
find the period of f(x)
find the domain of f(x)
find the range of f(x)

Please explain how you get your answers. Hopefully I'll understand them better!

Question 4 is basically a straightforward pattern recognition. Look up the definitions of amplitude, period, etc. in your text (or online). For instance, the amplitude is the constant in front of the trig function of the form Acos(ax - by). You need to understand those concepts, and how they impact the graph of those functions. Only through understanding the examples you are provided can you learn it, and it is a straight application of their definitions and functional form.

As for the other questions, they all stem from understanding the reference angle. It is a rather easy idea. Again, consult your textbook. The reference angle is the angle between the angle you're given (from 0, say) and the x-axis. So 30 degrees is just 30 degrees from the reference angle. Now suppose we have 150 degrees. It's reference angle is in relation to the x-axis it is nearest. In this case, how far is 150 from 180? In this case, the answer is the same as the last one: 30 degrees. This should come as no surprise as 150 and 30 are symmetric to each other between those two quandrants.

If you can understand that, and understand the information you are given, the solution is nothing more than simple arithmetic, mostly. It also helps to understand what the sin and cos represent on the unit circle. Try to answer the questions and let us know what progress you have made.

Originally Posted by danahamed

Math is definitely NOT my subject & my "teacher" CAN'T teach. So some help would be amazing! Here are some example questions I want to understand:

Well, these are really definition problems. It might be the student's responsibility to remember the definitions.

1. How do you find the reference angles for:
-190°
-3π/4
5π/8

What makes a reference angle a reference angle? What does "periodic" mean?

2. Are the following true or false & why?

cos(-175°) = cos(175°)
cos(32°) = sin(58°)
sin(π/3) = 1/sec(π/3)
cos(2π/3) = cos(4π/3)

What are the basic relationships between sine and cosine? Is cosine and odd function or an even function?

3. Given sinθ = -3/4 and θ is in quadrant 4, find the following:

cosθ
tanθ
sin (-θ)
cos (-θ)

This requires a Right Triangle and a little algebra. Please show your work.

4. Given the function, f(x) = 2cos(x/2)+3

find the amplitude of f(x)
find the period of f(x)
find the domain of f(x)
find the range of f(x)

What? No Phase Shift? Please show your work. Is this a quiz? You don't want to get my score and have your teacher believe you can do it unless you really can, do you?

Please explain how you get your answers. Hopefully I'll understand them better!

It will work better if you demonstrate some effort.

Actually, NO this isn't a quiz. These are example problems out of the book that I chose. Math is a really hard subject for me, hence why I even came to this website. Sadly, no help was offered. Thanks anyway.

You mean that no one simply worked the problems and handed you the solutions. Part of the study of mathematics is training your brain to think in a more organized and deliberate fashion. Memorizing techniques rarely accomplishes this.

I asked you four questions. Which did you answer? If you answer them, you will have received help. Giving help is not the same as receiving help. It takes effort from the reciever for the transaction to be complete. I gave you several other hints. Which did you heed?

Why did you "thank" bryangoodrich if you received no help? You should see this as illogical. We can help you with that if you will show some effort.