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O TRIGONOMETRIC IDENTITIES AND EQUATIONSMaDouble-angle identities: Problem type 1Es3Find sin 2x, cos 2x, and tan2x if tanx=and x terminates in quadrant III4sin 2x?cos2x=tan 2x=X

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O TRIGONOMETRIC IDENTITIES AND EQUATIONS
Ma
Double-angle identities: Problem type 1
Es
3
Find sin 2x, cos 2x, and tan2x if tanx=
and x terminates in quadrant III
4
sin 2x
?
cos2x
=
tan 2x
=
X
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O TRIGONOMETRIC IDENTITIES AND EQUATIONS Ma Double-angle identities: Problem type 1 Es 3 Find sin 2x, cos 2x, and tan2x if tanx= and x terminates in quadrant III 4 sin 2x ? cos2x = tan 2x = X

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Step 1

Since x is in 3rd quadrant, assume opposite of x= -3 and adjacent =-4

So hypotenuse= 5

(-3)+ C-4
-4
- 3
9+16
5
25
5
X
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(-3)+ C-4 -4 - 3 9+16 5 25 5 X

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Step 2

sin x= -3/5 and cos x= -4/5 

We use them in double angle formula.

Answer: sin 2x= 24/25 

3
sin 2x 2sin x cos x=2|
5
24
25
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3 sin 2x 2sin x cos x=2| 5 24 25

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Step 3

Answer: cos 2x...

3
16
9
7
4
cos 2x-cos?x - sin2x
1
25
25
5
25
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3 16 9 7 4 cos 2x-cos?x - sin2x 1 25 25 5 25

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