To the nearest tenth of a radian, determine possible values of θ in the domain -2π ≤ θ ≤ 2π where cot θ = 3/5.
By taking the tangent ratio (tan θ = 5/3) and inversing it, I get 1.0 radians on my calculator (set to radians mode). However, the textbook got 0.8. What did I do wrong? (I know how to calculate for the other possible angles!)
+36916 cot = 3/5 = cos/sin This can occur in Q I or Q III
Remember cos^2 + sin^2 = 1 ?
(3/x)^2 + (5/x)^2 = 1 x = sqrt 34 sin = 5/sqrt34 cos = 3/sqrt34 OR sin = - 5/sqrt34 and cos = - 3/sqrt34
(not sure why did all of that ....but there it is)
arctan 5/3 = 1.03 R AND 4.17 R
Not sure how text got that answer!
+36916 cot = 3/5 = cos/sin This can occur in Q I or Q III
Remember cos^2 + sin^2 = 1 ?
(3/x)^2 + (5/x)^2 = 1 x = sqrt 34 sin = 5/sqrt34 cos = 3/sqrt34 OR sin = - 5/sqrt34 and cos = - 3/sqrt34
(not sure why did all of that ....but there it is)
arctan 5/3 = 1.03 R AND 4.17 R
Not sure how text got that answer!
