If cos theta = 5/13 for x an acute angle, how do you find tan 2x exactly?

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If cos theta = 5/13 for x an acute angle, how do you find tan 2x exactly?

2007-12-16 10:50:20 · 2 answers · asked by cjbass21 1 in Science & Mathematics ➔ Mathematics

2 answers

cos Ө = 5 / 13
sin Ө = 12 / 13
tan Ө = 12 / 5

tan 2Ө = 2 tan Ө / (1 - tan ² Ө )
tan 2Ө = 24/5 / (1 - 144/25)
tan 2Ө = (24/5) / (-119 / 25)
tan 2Ө = - (24/5) (25/119)
tan 2Ө = - 120 / 119

2007-12-20 06:21:27 · answer #1 · answered by Como 7 · 0⤊ 0⤋

tan(2x)
= sin(2x) / cos(2x)
= 2sinxcosx / (2cos^2x -- 1)
= 2cosxâ (1 -- cos^2x) / (2cos^2x -- 1)
substitute 5/13 for cosx and calculate.

2007-12-16 19:05:34 · answer #2 · answered by sv 7 · 0⤊ 0⤋