Solving Trigonometric Equations: sin(θ) = 3/5

[MathRaven]

Spending my summer studying on my own, and I have come across some things which I would like to see how they are solved.
If you are capable of completing, please show work instead of just answers so that I can follow what you did, and take notes on it.

Homework Statement

If sin(θ) = 3/5 and θ is in Quad II, determine in EXACT form the following

a) sin(θ + π/6)

b) cos(5π/3 - θ)

c) cos(20)

d) csc(π/2 - θ)

 

[Villyer]

Does your course offer any double angle forumas or angle sum formulas?

 

[cepheid]

Clearly theta is part of a 3-4-5 triangle, which means that cos(theta) = 4/5.

These can all be solved by employing a set of trigonometric identities known as the sum and difference formulae, which tell you how to compute the sine or cosine of the *sum* (or difference) of two angles. Are you familiar with these identities?

 

[Villyer]

Clearly theta is part of a 3-4-5 triangle, which means that cos(theta) = 4/5.

Take into account the fact that the angle is in the second quadrant.

 

[cepheid]

Take into account the fact that the angle is in the second quadrant.

Good catch, I missed that.

 

[MathRaven]

well this is just me studying on my own, not really a course. . I want to study during the summer, and at some point in the future try to place.

Most of the things make sense, but I do have a list of problems that I haven't been able to complete.

I would like to see how you guys do them. .looking for answer, and how you got there, so i need to see the work for it.

 

[e^(i Pi)+1=0]

Spending my summer studying on my own, and I have come across some things which I would like to see how they are solved.
If you are capable of completing, please show work instead of just answers so that I can follow what you did, and take notes on it.

Homework Statement

If sin(θ) = 3/5 and θ is in Quad II, determine in EXACT form the following

a) sin(θ + π/6)

b) cos(5π/3 - θ)

c) cos(20)

d) csc(π/2 - θ)

Is that symbol supposed to be pi?

 

[cepheid]

well this is just me studying on my own, not really a course. . I want to study during the summer, and at some point in the future try to place.

Most of the things make sense, but I do have a list of problems that I haven't been able to complete.

I would like to see how you guys do them. .looking for answer, and how you got there, so i need to see the work for it.

Even if this is not actual homework, it's still against forum rules for us to provide a complete solution for you. We've given you an important hint: if you're learning on your own, then look up the sum and difference formulas: how might they be applied to this problem? Answer that question, and you'll be on your way.

To e^ipi + 1 = 0: yes, that symbol is the way lowercase pi looks in the default forum font. If you use times roman, it looks a bit better: π

 

[Villyer]

well this is just me studying on my own, not really a course. . I want to study during the summer, and at some point in the future try to place.

Most of the things make sense, but I do have a list of problems that I haven't been able to complete.

I would like to see how you guys do them. .looking for answer, and how you got there, so i need to see the work for it.

Unfortunately we aren't supposed to do the work for you, we can only give you hints and pointers.
Look up the double angle formulas and the sum and difference formulas.
(cepheid beat me to this point)Also, do you understand how to find cos(θ) from the information given?

 

[Mark44]

If you are capable of completing, please show work instead of just answers so that I can follow what you did, and take notes on it.

That's not the way it works here at Physics Forums.

The following is from the Rules (click Rules near the top of the window). Emphasis added.

On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.