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secondary 4 | A Maths
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Date Posted: 2 years ago
Views: 161
Alternative method : R-formula
tan x + √3 = sec x
sin x / cos x + √3 = 1/cos x
sin x + √3 cos x = 1
R = √((√3)² + 1²) = √(3 + 1) = √4 = 2
α = tan-¹ (√3/1) = tan-¹ (√3) = 60°
So,
sin x + √3 cos x = 2sin(x + 60°) = 1
sin(x + 60°) = ½
(positive, so look at the first and second quadrant)
x + 60° = sin-¹ (½)
Basic angle = 30°
Since 0° ≤ x ≤ 360°, then 60° ≤ x + 60° ≤ 420°
x + 60° = 180° - 30°, 360° + 30°
x + 60° = 150°, 390°
x = 90°, 330°
(Reject 90° as it does not satisfy the original equation)
So x = 330°
tan x + √3 = sec x
sin x / cos x + √3 = 1/cos x
sin x + √3 cos x = 1
R = √((√3)² + 1²) = √(3 + 1) = √4 = 2
α = tan-¹ (√3/1) = tan-¹ (√3) = 60°
So,
sin x + √3 cos x = 2sin(x + 60°) = 1
sin(x + 60°) = ½
(positive, so look at the first and second quadrant)
x + 60° = sin-¹ (½)
Basic angle = 30°
Since 0° ≤ x ≤ 360°, then 60° ≤ x + 60° ≤ 420°
x + 60° = 180° - 30°, 360° + 30°
x + 60° = 150°, 390°
x = 90°, 330°
(Reject 90° as it does not satisfy the original equation)
So x = 330°
See 3 Answers
150° actually doesn't satisfy the original equation when substituted .
See alternative method in main comments
done
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clear
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Momo's working is short and simple. Just an addition to your working.
Date Posted:
2 years ago
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