Given: theta in [pi /2, pi ] and tan theta = 1/3. Find sin theta and cos theta (but to find theangle is not needed)

Samson Kaufman 2022-08-04 Answered
Given: θ [ π / 2 , π ] and tan θ = 1 / 3.
Find sin θ and cos θ (but to find the angle is not needed)
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Answers (2)

pelvogp
Answered 2022-08-05 Author has 18 answers
Given: θ [ π / 2 , π ] and tan θ = 1 / 3.
Find sin θ and cos θ (but to find theangle is not needed)
tan θ = 1 / 3 h y p = 9 + 1 = 10
sin θ = 1 / 10
cos θ = 3 / 10

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traucaderx7
Answered 2022-08-06 Author has 2 answers
we have two solutions to the question
tan θ = 1 / 3
clearly we have a right angle triangle with
p=1, b=3
thus h = 3 2 + 1 2 = ± 10
so either cos θ = 3 / 10 , sin θ = 1 / 10
or cos θ = 3 / 10 , sin θ = 1 / 10
if n is specified then θ and thus exact solution can be determined

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