Question

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

Answer 1

`=>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`

Answer 2

`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`

Answer 3

`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"`

Answer 4

`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)