1084 Ange funktionernas maximi- och minimipunkter för \( 0^{\circ} \leq x \leq 360^{\circ} \) a) \( f(x)=5 \sin \left(x+20^{\circ}\right) \) b) \( f(x)=3 \sin \frac{x}{2} \) c) \( f(x)=1-0,5 \cos \left(x+50^{\circ}\right) \) d) \( f(x)=2,75 \sin 3\left(x+15^{\circ}\right)+0,25 \)

Här är maximi- och minimipunkterna för de angivna funktionerna inom intervallet \( 0^{\circ} \leq x \leq 360^{\circ} \): a) \( f(x) = 5 \sin \left(x + 20^{\circ}\right) \) - **Maximipunkt:** \( x = 70^{\circ} \), \( f(x) = 5 \) - **Minimipunkt:** \( x = 250^{\circ} \), \( f(x) = -5 \) b) \( f(x) = 3 \sin \left(\frac{x}{2}\right) \) - **Maximipunkt:** \( x = 180^{\circ} \), \( f(x) = 3 \) - **Minimipunkter:** \( x = 0^{\circ} \) och \( x = 360^{\circ} \), \( f(x) = 0 \) c) \( f(x) = 1 - 0{,}5 \cos \left(x + 50^{\circ}\right) \) - **Maximipunkt:** \( x = 130^{\circ} \), \( f(x) = 1{,}5 \) - **Minimipunkt:** \( x = 310^{\circ} \), \( f(x) = 0{,}5 \) d) \( f(x) = 2{,}75 \sin \left(3\left(x + 15^{\circ}\right)\right) + 0{,}25 \) - **Maximipunkter:** \( x = 15^{\circ} \), \( 135^{\circ} \), \( 255^{\circ} \), \( f(x) = 3 \) - **Minimipunkter:** \( x = 75^{\circ} \), \( 195^{\circ} \), \( 315^{\circ} \), \( f(x) = -2{,}5 \) Sammanfattning: | Funktion | Typ | \( x \) (°) | \( f(x) \) | |-----------------------------------------|-----------|---------------------|--------------| | \( 5 \sin (x + 20^{\circ}) \) | Maximum | \( 70^{\circ} \) | \( 5 \) | | | Minimum | \( 250^{\circ} \) | \( -5 \) | | \( 3 \sin \left(\frac{x}{2}\right) \) | Maximum | \( 180^{\circ} \) | \( 3 \) | | | Minimum | \( 0^{\circ}, 360^{\circ} \) | \( 0 \) | | \( 1 - 0{,}5 \cos (x + 50^{\circ}) \) | Maximum | \( 130^{\circ} \) | \( 1{,}5 \) | | | Minimum | \( 310^{\circ} \) | \( 0{,}5 \) | | \( 2{,}75 \sin (3(x + 15^{\circ})) + 0{,}25 \) | Maximier | \( 15^{\circ}, 135^{\circ}, 255^{\circ} \) | \( 3 \) | | | Minimier | \( 75^{\circ}, 195^{\circ}, 315^{\circ} \) | \( -2{,}5 \) | Om du har fler frågor eller behöver mer information, tveka inte att fråga!