tatumkays tatumkays

11-04-2024
Mathematics

Answered

find all exact solutions on [0,2pi) for 2sin(2x)+3sinx=0

Answer :

olumideolawoyin olumideolawoyin

11-04-2024

Answer:

x = 138.6° or 221.4°

Step-by-step explanation:

2sin2x + 3sinx = 0

(From trigonometry identity: sin2x = 2sinxcosx, therefore, 2sin2x = 4sinxcosx)

4sinxcosx + 3sinx = 0

4sinxcosx = -3sinx

4cosx = -3 (Divide both sides by sinx)

cosx = -3/4

x = arccos(-3/4)

x = 138.6° ( Second quadrant) or

x = 41.4 + 180 = 221.4° (Third quadrant).

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