Mathematics: If 0≤β 2π, find all values of β that satisfy the equation cos(2β)=√3/2

If 0≤β 2π, find all values of β that satisfy the

Ответ:

masonprice

30.01.2022

π/12 rad and 23π/12 rad

Step-by-step explanation:

Given the expression cos(2β)=√3/2 for 0≤β<2π, we are to find the value of β within the range that satisfies the equation.

$cos(2\beta)=\sqrt{ 3}/2\\\\take \ the\ arccos\ of \ both \ sides\\\\cos^{-1}cos(2\beta) = cos^{-1}\sqrt{{3} }/2 \\ \\2\beta = cos^{-1}\sqrt{{3} }/2 \\\\2\beta = 30^0\\\\\beta = 30/2\\\\\beta = 15^0$

Since cos id positive in the 4th quadrant, $\beta = 360^0-15^0$ , $\beta = 345^0$

Hence the value of $\beta$ that satisfy the equation are 15° and 345°

Converting to radians;

180° = πrad

15° = 15π/180 rad

15° = π/12 rad

345° = 345π/180

345° = 23π/12 rad

The values in radians are π/12 rad and 23π/12 rad

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Ответ:

tobyclyde

30.07.2020

Mathematics

Step-by-step explanation:

If it's 3 cupcakes for 1 person and you have 2 people, then you need 6 cupcakes.

Hope this helps! Plz give brainliest!

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If 0≤β<2π, find all values of β that satisfy the equation cos(2β)=√3/2

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