Answer:
i think it should be tan2x = 24/7, i hope i am not wrong
Step-by-step explanation:
If sin x = -3/5 and x is in quadrant 3, then tan 2x = 24/7.
Given:
[tex]$Sin x = \frac{-3}{5}[/tex]
To estimate cos x by identity
[tex]$Cos^{2} x=1-Sin^{2} x[/tex]
[tex]$Cos^{2} x =1-\frac{9}{25}[/tex]
[tex]$=\frac{16}{25}[/tex]
cos x = ±(4/5)
Since x exists in Quadrant III, then cos x exists negative.
tan x = Sin x/Cos x
= (−35)/(−54) = 3/4
By using the trigonometric identity, we get
tan 2x = 2 tan x / [tex]$1-tan^{2} x[/tex]
tan 2x = (6/4) / (1−9/16)
= (6/4)(16/7)
= 24/7
Therefore, tan 2x = 24/7.
To learn more about trigonometric identity
https://brainly.com/question/25024376
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