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28 votes
28 votes
Given cos theta=4sqrt2/7 find sin theta

User Cristian Curti
by
2.8k points

2 Answers

14 votes
14 votes


\\ \rm\Rrightarrow cos\theta=(4√(2))/(7)

Now


\\ \rm\Rrightarrow sin^2\theta=1-cos^2\theta


\\ \rm\Rrightarrow sin^2\theta=1-(16(2))/(49)


\\ \rm\Rrightarrow sin^2\theta=1-(32)/(49)


\\ \rm\Rrightarrow sin^2\theta=(17)/(49)


\\ \rm\Rrightarrow sin\theta=(√(17))/(7)

User Chintan Adatiya
by
2.6k points
17 votes
17 votes

Answer:


  • sin \theta=√(17)/7

Explanation:

Given


  • cos \theta=4√(2)/7

Find


  • sin \theta

Solution

Use identity:


  • sin^2x+cos^2x=1

Substitute and find:


  • cos^2 \theta=(4√(2)/7)^2

  • cos^2 \theta=16*2/49=32/49


  • sin \theta=√(1-cos^2 \theta) = √(1-32/49) =√(17/49) =√(17)/7

User Masto
by
2.9k points