If cos theta =2/3,find theta where 180°<theta<360° What is the theta?

4 Answers
maganbhai P.
May 6, 2018

#=>theta=(311.81)^circ#

Explanation:

Here,

#costheta =2/3 > 0=>I^(st) Quadrant or color(red)(IV^(th) Quadrant...to(A)#

But,

#180^circ < theta < 360^circ=>III^(nd)Quadran or color(red)(IV^(th)Quadrant to(B)#

From #color(red)((A) and(B)#,we can say that

#270^circ < theta < 360^circtocolor(red)(IV^(th) Quadrant#

Hence,

#costheta=2/3=>theta=360^circ-cos^-1(2/3)=360^circ-(48.19)^circ#

#=>theta=(311.81)^circ#

Dean R.
May 6, 2018

#180^circ < theta < 360^circ,# means third or fourth quadrant. A positive cosine means first or fourth quadrant. So fourth quadrant:

#theta = 360^circ - text{Arc}text{cos}(2/3) approx 311.8^circ #

Jim G.
May 6, 2018

#theta=311.8^@" to 1 dec. place"#

Explanation:

#"since "costheta>0" then "theta" is in the first or"#
#"fourth quadrant"#

#"given "180^@ < theta<360^@" we require "theta" in the"#
#"fourth quadrant"#

#theta=cos^-1(2/3)=48.2^@larrcolor(red)"in first quadrant"#

#rArrtheta=(360-48.2)=311.8^@larrcolor(red)"in fourth quadrant"#

Nghi N
May 6, 2018

#t = 311^@81#

Explanation:

#cos t = 2/3#
Calculator and unit circle give 2 solutions for t:
#t = +- 48^@19#
In the interval (180, 360), the answer is:
#t = - 48^@19#,
or #t = 360^@ - 48^@ 19 = 311^@81# (co-terminal to - 48.19)

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