# Math

if sin theta =1/2 and cos theta= √(3)/2. find tha values of tan θ, cot θ, sec θ and cscθ.

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1. can someone show me the answer to tanθ and cotθ
my answer to secθ is 2/√3 and cscθ is 2

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2. Both sin theta and cos theta are positive, so theta must be in quad I
construct your right-angled triangle with opposite as 1 and hypotenuse as 2
and use Pythagoras to find the adjacent to be √3 .
So now simply use the definitions of the trig ratios to find the other 4 missing ratios.

eg sec theta = hypotenuse/adjacent = 2/√3

btw, memorize SOH CAH TOA

let me know what you get

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posted by Reiny
3. my answers are
secθ is 2/√3
cscθ is 2
i really don't know how to get tanθ and cot θ

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4. the tanθ is 22.20
cot θ is 1/22.20

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5. How can you possibly come up with those numbers ?? They are not even sides of the triangle.
the others are correct

tan θ = opp/adj = 1/√3 and cot θ = √3

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posted by Reiny
6. i did tan^-1 ((1/2)/(√(3)/2)) on my calculator

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7. tan^-1 ((1/2)/(√(3)/2)) would have given you the angle

Of course that angle would obviously be 30 degrees, not 22.2

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posted by Reiny
8. sin A = 1/2 = Y/r.
Cos A = sqrt3/2 = X/r.
x = sqrt 3, Y = 1, r = 2.

Tan A = Y/X = 1/sqrt3.
Cot A = 1/Tan A = sqrt3/1 = sqrt 3.
sec A = 1/Cos A = 2/sqrt 3.
csc A = 1/sin A = 2/1 = 2.

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posted by henry2,

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