Help with a simple trig problem.

[Awnsymnta]

Hi, I would like some help on how to solve this kind of trigonometry problem. Let's say they tell you to find cos(x+y) and they give you cos(x)=5/13 and sec(y)=5/4, I can do it and get my answer in irrational decimals, but my problem is that they want the answer in rational form and the values of x and y are between 0 and pi/2. What is the method to solving this?

Also if you could link me to a youtube lesson or playlist that can teach me this stuff it would be much appreciated.

Thank you

 

[Deleted member 4993]

Hi, I would like some help on how to solve this kind of trigonometry problem. Let's say they tell you to find cos(x+y) and they give you cos(x)=5/13 and sec(y)=5/4, I can do it and get my answer in irrational decimals, but my problem is that they want the answer in rational form and the values of x and y are between 0 and pi/2. What is the method to solving this?

Also if you could link me to a youtube lesson or playlist that can teach me this stuff it would be much appreciated.

Thank you

Decimals are by definition rational numbers.

You cannot guarantee rational answer - but the particular problem you spoke of has answer with rational number.

sec(y) = 5/4

cos(y) = 4/5 ... then sin(y) = 3/5 (all positive because x and y are in first quadrant)

cos(x) = 5/13 ... then sin(x) = 12/13 (all positive because x and y are in first quadrant)

Now expand cos(x+y) and calculate its value.

 

[Awnsymnta]

How to expand?

Decimals are by definition rational numbers.

You cannot guarantee rational answer - but the particular problem you spoke of has answer with rational number.

sec(y) = 5/4

cos(y) = 4/5 ... then sin(y) = 3/5 (all positive because x and y are in first quadrant)

cos(x) = 5/13 ... then sin(x) = 12/13 (all positive because x and y are in first quadrant)

Now expand cos(x+y) and calculate its value.

What you mean expand?

 

[Awnsymnta]

Would someone help me out?

Help, I am utterly lost on how to solve these problems, I am sure they are easy, I just don't know the material. Please help me. Using your knowledge of trigonometric identities, find the exact value of cos(x+y) knowing that x and y are between 0 and π/2, that cos(x)=5/13 and that sec(y)=5/4. Your answer must be a rational number, written in the form of an irreducible fraction p/q (such as 2/3, 4/5, −1/4, etc.), with q>0. Give the integers p and q. Using your knowledge of trigonometric identities, find the exact value of sin(2x) knowing that x is between 0 and π/2 and that sin(x)=7/25. Your answer must be a rational number, written in the form of an irreducible fraction p/q (such as 2/3, 4/5, −1/4, etc.), with q>0. Give the integers p and q. I can solve it but I will get a really large decimal, I need the method to get a nice rational answer.

 

[Deleted member 4993]

What you mean expand?

cos(A+B) = cos(A) *cos(B) - sin(A)*sin(B)