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:
enter image source here

Jun 27, 2018

cos(theta)= -0.83147941928309808568527749607034

= -0.8315 (4dp)

Explanation:

Find theta (Note: there are 2 possible angles for sin(theta) = 5/9 )
Sin^-1(5/9) = 33.748988595888587817404332744458 (degrees)

The sin will also have the value (5/9) at

180-33.748988595888587817404332744458

=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 theta is the 146.25101.... value)

Jun 27, 2018

costheta=-sqrt56/9

Explanation:

"using the "color(blue)"trigonometric identity"

•color(white)(x)sin^2theta+cos^2theta=1

rArrcostheta=+-sqrt(1-sin^2theta)

"given "sintheta=5/9" and "costheta<0

"then "theta" is in the second quadrant"

costheta=-sqrt(1-(5/9)^2)

color(white)(costheta)=-sqrt(1-25/81)

color(white)(costheta)=-sqrt(56/81)=-sqrt56/9