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secondary 3 | A Maths
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A math : trigonometric equation, identities and addition formulae
Date Posted: 3 years ago
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0 ≤ x ≤ 4π
0 ≤ 2x ≤ 8π
π/12 ≤ 2x + π/12 ≤ 8π + π/12
π/12 ≤ 2x + π/12 ≤ 97π/12
sin (2x + π/12) = 0.3 (positive, so consider 1st and 2nd quadrants)
2x + π/12 = sin-¹ (0.3)
Basic angle θ ≈ 0.3047
2x + π/12 ≈ 0.3047 , π - 0.3047, 2π + 0.3047, 3π - 0.3047, 4π + 0.3047, 5π - 0.3047, 6π + 0.3047, 7π - 0.3047 (stop here as the next one will exceed the domain of x)
x ≈ (0.3047 - π/12)/2 , (π - 0.3047 - π/12)/2 , (2π + 0.3047 - π/12)/2 , (3π - 0.3047 - π/12)/2, (4π + 0.3047 - π/12)/2 , (5π - 0.3047 - π/12)/2 , (6π + 0.3047 - π/12)/2, (7π - 0.3047 - π/12)/2
x ≈ 0.0215, 1.29, 3.16, 4.43, 6.30, 7.57, 9.45, 10.7 (3s.f)
All units in radians
0 ≤ 2x ≤ 8π
π/12 ≤ 2x + π/12 ≤ 8π + π/12
π/12 ≤ 2x + π/12 ≤ 97π/12
sin (2x + π/12) = 0.3 (positive, so consider 1st and 2nd quadrants)
2x + π/12 = sin-¹ (0.3)
Basic angle θ ≈ 0.3047
2x + π/12 ≈ 0.3047 , π - 0.3047, 2π + 0.3047, 3π - 0.3047, 4π + 0.3047, 5π - 0.3047, 6π + 0.3047, 7π - 0.3047 (stop here as the next one will exceed the domain of x)
x ≈ (0.3047 - π/12)/2 , (π - 0.3047 - π/12)/2 , (2π + 0.3047 - π/12)/2 , (3π - 0.3047 - π/12)/2, (4π + 0.3047 - π/12)/2 , (5π - 0.3047 - π/12)/2 , (6π + 0.3047 - π/12)/2, (7π - 0.3047 - π/12)/2
x ≈ 0.0215, 1.29, 3.16, 4.43, 6.30, 7.57, 9.45, 10.7 (3s.f)
All units in radians
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