Βασικές Τριγωνομετρικές Εξισώσεις

Απλές Εξισώσεις

Να επιλυθούν οι εξισώσεις.

\(  \begin {array} {llllll}
\color {#ff6600} { \mathcal { i) }} \: ημθ =  \cfrac {1} {2}  &
\color {#ff6600} { \mathcal { ii) }} \: ημθ = – \cfrac {1} {2}  &
\color {#ff6600} { \mathcal { iii) }} \: 2ημ^2θ = 1  &  \\[3ex] \color {#ff6600} { \mathcal { iv) }} \: 2ημθ + \sqrt{3} = 0  \hspace {8mm} (Απ: θ = 2κπ – π/3, θ = 2κπ -2π/3)  &
\color {#ff6600} { \mathcal { v) }} \: ημθ = – \cfrac {\sqrt {3}} {2}  &   \\[3ex] ​\color {#ff6600} { \mathcal { vi) }} \: 2ημ^2θ – 3ημθ + 1 = 0   \hspace {8mm}   \left (Απ: θ = 2κπ + \cfrac {π} {2}, θ = 2κπ + \cfrac {π} {6}, θ = 2κπ + \cfrac {5π} {6}  \right ) &
\end {array}  \)

 

Να επιλυθούν οι εξισώσεις.

\(  \begin {array} {llllll}
\color {#ff6600} { \mathcal { i) }} \: συνθ = 1  &
\color {#ff6600} { \mathcal { i) }} \: 2συνθ – 1 = 0  \hspace {8mm}  (Απ: θ = 2κπ + π/3, θ = 2κπ + 5π/3) &
\color {#ff6600} { \mathcal { ii) }} \: συνθ = \cfrac {\sqrt {2}} {4}  &  \\[3ex] \color {#ff6600} { \mathcal { iii) }} \: συνθ = \cfrac {\sqrt {2}} {2}  &
\color {#ff6600} { \mathcal { iv) }} \:  συνθ = – \cfrac {\sqrt {2}} {2} &   \\[3ex] \end {array}  \)

 

Να επιλυθούν οι εξισώσεις.

\(  \begin {array} {llllll}
\color {#ff6600} { \mathcal { i) }} \: εφθ = 1  &
\color {#ff6600} { \mathcal { i) }} \: ημθ = συνθ  \hspace {8mm}  \left ( Απ: θ = κπ + \cfrac {π} {4}  \right )   &
\color {#ff6600} { \mathcal { ii) }} \: εφθ = -\sqrt {3}  &   \\[3ex] \color {#ff6600} { \mathcal { iv) }} \: εφ^2θ = 3  &
\color {#ff6600} { \mathcal { iv) }} \: εφ^2θ – εφθ = 0  &   \\[3ex] ​\color {#ff6600} { \mathcal { v) }} \: εφ \left  ( θ – \cfrac {π} {2}  \right ) = 1  \hspace {8mm}  \left ( Απ: θ = κπ + \cfrac {3π} {4}  \right )    &
\end {array}  \)

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