Find all solutions to the equation:

\(\csc^2 \theta - 4 = 0\)

cse c 2 β − 4 = 0 ( csec β − 2 ) ( csec β + 2 ) = 0 #1 csec β − 2 = 0 csec β = 2 β = − 1.099 ​ #2 csec β + 2 = 0 csec β = − 2 β = 1.099 ​

Answered by mariamikayla | 2024-06-10

I am replacing θ with A, so don't get confused cs c 2 A − 4 = 0
cs c 2 A − 2 2 = 0
( csc A + 2 ) ( csc A − 2 ) = 0
Using zero product property: EITHER csc A + 2 = 0 csc A = − 2 A = − 30 °
OR csc A − 2 = 0 csc A = 2 A = 30 °

Answered by rabinshrestha41 | 2024-06-10

The solutions to the equation csc 2 θ − 4 = 0 are found by setting csc 2 θ = 4 , which leads to sin 2 θ = 4 1 ​ . The resulting angles are 3 0 ∘ , 15 0 ∘ , 21 0 ∘ , and 33 0 ∘ plus any multiple of 36 0 ∘ .
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Answered by mariamikayla | 2024-12-26