J's answer to tricia's Secondary 4 A Maths Singapore question.
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See question's comments section for two ways to prove.
As for the second part,
(sin A + 1) / cos A = 3 cos A
sin A + 1 = 3 cos² A
sin A + 1 = 3 - 3 sin² A
3 sin² A + sin A - 2 = 0
(3 sin A - 2)(sin A + 1) = 0
3 sin A = 2 or sin A = -1
sin A = ⅔ or sin A = -1
For sin A = ⅔, Basic angle = sin-¹ (⅔) ≈ 0.7297 rad
Since sin A is positive, look at first and second quadrant
A ≈ 0.7297 rad or A ≈ π - 0.7297 rad
A = 0.730 rad (3s.f) or A ≈ 2.412 rad = 2.41 rad (3s.f)
For sin A = -1, A = 3π/2 (you should know that the sin x graph cuts y = -1 at x = 3π/2 and this repeats every 2π radians)
As for the second part,
(sin A + 1) / cos A = 3 cos A
sin A + 1 = 3 cos² A
sin A + 1 = 3 - 3 sin² A
3 sin² A + sin A - 2 = 0
(3 sin A - 2)(sin A + 1) = 0
3 sin A = 2 or sin A = -1
sin A = ⅔ or sin A = -1
For sin A = ⅔, Basic angle = sin-¹ (⅔) ≈ 0.7297 rad
Since sin A is positive, look at first and second quadrant
A ≈ 0.7297 rad or A ≈ π - 0.7297 rad
A = 0.730 rad (3s.f) or A ≈ 2.412 rad = 2.41 rad (3s.f)
For sin A = -1, A = 3π/2 (you should know that the sin x graph cuts y = -1 at x = 3π/2 and this repeats every 2π radians)
Date Posted:
3 years ago
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