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⇒θ=(311.81)∘

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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