Compute angles, trignometry/pre-calc?

[Matriculator]

Homework Statement

I'm having a problem with this. I was told to use the difference of sums formula. I'm not exactly sure of what that is/means.

Homework Equations

Difference of sums?

The Attempt at a Solution

I'm thinking that Cos(a)=1/3 refers to 1 being the adjacent angle and 3 is the hypotenuse. Therefore the opposite angle equals to sqrt(3²-1²). Or does 1/3 somehow correspond to an angle? a or alpha should be 30 degrees then right? I need a lead-in. From there, I think that I'll be able to take it form there. Than you in advance.

 

[SteamKing]

You are making this more complicated than necessary:

cos(a) = 1/3 = 0.3333...

Sometimes a cigar is just a cigar.

 

[Matriculator]

You are making this more complicated than necessary:

cos(a) = 1/3 = 0.3333...

Sometimes a cigar is just a cigar.

Lol, this is why I often miss a lot of points on tests, my minds always on "it's not that easy mode". But how does that go into helping me figure out the other problems(In the picture)? Being on that mode again, I'm thinking that it's not as easy as just subtracting and replacing the signs. Thank you.

 

[Mark44]

Homework Statement

I'm having a problem with this. I was told to use the difference of sums formula. I'm not exactly sure of what that is/means.

Homework Equations

Difference of sums?

The Attempt at a Solution

I'm thinking that Cos(a)=1/3 refers to 1 being the adjacent angle and 3 is the hypotenuse. Therefore the opposite angle equals to sqrt(3²-1²).

No, the opposite side is sqrt(3²-1²). To get the opposite angle, find angle a using the inverse cosine function, and then subtract a from $\pi$/2.

Or does 1/3 somehow correspond to an angle? a or alpha should be 30 degrees then right? I need a lead-in. From there, I think that I'll be able to take it form there. Than you in advance.

 

[eumyang]

The beginning of the problem states:

Given an angle π in the first quadrant...

... which makes no sense. The terminal side of an angle of π radians (or 180°) would be on the negative x-axis, between the 2nd and 3rd quadrants. Do you mean to say,
"Given an angle a in the first quadrant..."?

 

[Matriculator]

The beginning of the problem states:

... which makes no sense. The terminal side of an angle of π radians (or 180°) would be on the negative x-axis, between the 2nd and 3rd quadrants. Do you mean to say,
"Given an angle a in the first quadrant..."?

Yes, sorry about that. It was a stupid copy and paste of Pi, I mean a.

 

[SteamKing]

You do know the sum and difference formulas for calculating the sine and cosine of angle sums and angle differences, don't you?