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# Determining the possible values for θ?

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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!)

Mar 22, 2020

#1
+23710
+1

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!

Mar 22, 2020

#1
+23710
+1

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!

ElectricPavlov Mar 22, 2020