﻿ If theta is an acute angle such that sin theta=5/13, what is the value of sin2 theta - Science Mathematics
If theta is an acute angle such that sin theta=5/13, what is the value of sin2 theta
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# If theta is an acute angle such that sin theta=5/13, what is the value of sin2 theta

[From: ] [author: ] [Date: 11-04-25] [Hit: ]
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cosӨ= 12/13

sin 2Ө= 2 sinӨcosӨ = 2 (5/13)(12/13) = 120/169

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sin(2a) = 2sin(a)cos(a)

now since a is acute and cos(a) = sqrt(1 - (5/13)^2)

=> cos(a) = 12/13

=> sin(2a) = 2sin(a)cos(a) = 2 * (5/13) * (12/13) = 120/169

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sin2theta = 2 sin theta cos theta

then you have to fin the value of cos theta

which is root 1-25/13^2 unit circle

12/13

then sin 2 theta = 2 * 5/13 * 12/13
= 12/169
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