find the exact values of \sin 2u, \cos 2u, and

Algotssleeddynf 2021-12-15 Answered
find the exact values of sin2u,cos2u, and tan2u using the double-angle formulas. tanu=35,0<u<π2
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Expert Answer

poleglit3
Answered 2021-12-16 Author has 32 answers

Step 1
Given data are: tanu=35, u is in 1. quadrant.
So we have:
tanu=35
sinucosu=35
sinu=35cosu
sin2u+cos2u=1 use: sinu=35cosu
3425cos2u=1
cos2u=2534{
cosu=±534u is in 1. quadrant
cosu=534sinu=334
Step 2
We can now calculate what is required in the:
sin2u=2sinucosu
=2334534
=1517
cos2u=cos2usin2u
=2534934
=817
tan2u=2tanu1tan2u
=2351925
=158

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censoratojk
Answered 2021-12-17 Author has 46 answers
Given: tan(u)=35,0<u<π2
Angle u is in quadrant 1. A right triangle can be drawn is quadrant 1. Since tan(u)=35, the side opposite angle u is 3 and the side adjacent to angle u is 5. Using the pythagorean theorem the hypotenuse of the triangle is 34.
sin(2u)=2sin(u)cos(u)=2(334)(534)=3034=1517
cos(2u)=12sin2(u)=12(334)2=11834=34341834=1634=817
tan(2u)=3tan(u)1tan2(u)=2(35)1(35)2=651925=652525925=651625=158
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