Can someone help me answer this question? 'find the exact value of Cos theta, given sin theta = 5/9 and cos theta < 0

3 Answers
Jun 27, 2018

I got 0.831

Explanation:

Have a look:
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Jun 27, 2018

cos(θ)=0.83147941928309808568527749607034

= -0.8315 (4dp)

Explanation:

Find θ (Note: there are 2 possible angles for sin(θ)=59)
sin1(59)=33.748988595888587817404332744458(degrees)

The sin will also have the value (59) at

18033.748988595888587817404332744458

=146.25101140411141218259566725554(degrees)

If you are not sure which of these angles will have cos < 1, try both.
(note that the numbers for both angles are actually the same but one is positive and the other is negative)

cos(33.748988595888587817404332744458)
=0.83147941928309808568527749607034

cos(146.25101140411141218259566725554)
=0.83147941928309808568527749607034

(so θ is the 146.25101.... value)

Jun 27, 2018

cosθ=569

Explanation:

using the trigonometric identity

xsin2θ+cos2θ=1

cosθ=±1sin2θ

given sinθ=59 and cosθ<0

then θ is in the second quadrant

cosθ=1(59)2

cosθ=12581

cosθ=5681=569