Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# help with this trig question!? Relevance
• Anonymous
1 month ago

x = 2/3.......

• Login to reply the answers
• cos x=5/13, sin x= sqrt(13^2-5^2)/13=12/13. Tan x= 12/5

• Login to reply the answers
• Anonymous
1 month ago

The easiest way to solve this is with the tangent half angle formula (they are really 3 formulas below):

tan(Ѳ/2) = ±√((1 - cos(Ѳ))/(1 + cos(Ѳ))) = sin(Ѳ)/(1-cos(Ѳ)) = csc(Ѳ) - cot(Ѳ)

https://en.wikipedia.org/wiki/List_of_trigonometri...

The first one, ±√((1 - cos(Ѳ))/(1 + cos(Ѳ))), is what you need, since you know

cos(Ѳ) = 5/3.

So just plug it in:

tan(Ѳ/2) = ±√((1 - (5/3))/(1 + (5/3)))

There are 2 potential solutions, a positive and negative one.

There are a lot of trig identities, and it's hard to remember them all. If you can, I recommend looking them up from a table. If you have to memorize them, then memorize the most basic ones first, and try to be able to derive the more complicated ones without needing to memorize them.

Source(s): Blessed enough to go to school
• Login to reply the answers