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Find two solutions of the equation. Give your answers in degrees (0° ≤ θ < 360°) and in radians (0 ≤ θ < 2π). Do not use a calculator. (Do not enter your answers with degree symbols.)

(a) cos θ = √2/2

degrees (sm & lg values) radians (sm & lg)

(b) cos θ = - √2/2

degrees (sm & lg values) radians (sm & lg)

Respuesta :

a) In degrees the values are 45° and 315°

In radians values are [tex]\frac{\pi}{4}[/tex] and [tex]\frac{7\pi}{4}[/tex]

b) In degrees the values are 135° and 225°

   In radians values are [tex]\frac{3\pi}{4}[/tex] and [tex]\frac{5\pi}{4}[/tex]

Step-by-step explanation:

a) cos θ = √2/2

   That is

               [tex]cos\theta =\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}\\\\\theta=cos^{-1}\left ( \frac{1}{\sqrt{2}}\right )[/tex]

   In degrees the values are 45° and 315°

   [tex]\texttt{In radians values are }\frac{\pi}{4}\texttt{ and }\frac{7\pi}{4}[/tex]

b) cos θ = -√2/2

   That is

               [tex]cos\theta =\frac{-\sqrt{2}}{2}=-\frac{1}{\sqrt{2}}\\\\\theta=cos^{-1}\left ( -\frac{1}{\sqrt{2}}\right )[/tex]

   In degrees the values are 135° and 225°

   [tex]\texttt{In radians values are }\frac{3\pi}{4}\texttt{ and }\frac{4\pi}{4}[/tex]

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