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May 9th, 2019, 01:04 PM   #1
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Trigonometric Quadrant

Suppose that A is a second quadrant angle with sin A = 1/4. Determine the exact value of sin(A/2).
The problem has made me crazy. Help please

Last edited by Khoxy; May 9th, 2019 at 01:11 PM.
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May 9th, 2019, 01:44 PM   #2
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$\sin\frac{A}{2}=\sqrt{\frac{1-\cos A}{2}}$ where $\cos A=-\sqrt{\frac{15}{16}}$. The sign for $\cos A$ is negative, since $A$ is in the second quadrant.

Ans.=0.984250984251476

Last edited by skipjack; May 9th, 2019 at 01:59 PM.
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May 9th, 2019, 02:02 PM   #3
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Mathman I don't understand how you come up with cos A. Would you clarify?
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May 9th, 2019, 02:10 PM   #4
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cos²(A) ≡ 1 - sin²(A) and cos(A) ≡ 1 - 2sin²(A/2)

$\sqrt{\small8 + 2\sqrt{15}}/\small4 = 0.9920$...
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May 10th, 2019, 12:49 PM   #5
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$\sin{\frac{A}{2}}=0.992029696267167$ Arith. error in previous.

$\cos^2A=1-\sin^2A=1-\frac{1}{16}=\frac{15}{16}$.

Last edited by skipjack; May 10th, 2019 at 10:35 PM.
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