Determine the period and phase angle for the function y = 6sin(x/2 − 90°).

Question

ScanSolve AI Tutor · Accepted Answer

Ili kubaini kipindi na pembe ya awamu ya kazi ya trigonometric $y = A\sin(Bx - C) + D$ , tunatumia fomula zifuatazo:

Kipindi (Period) $= \frac{360^\circ}{|B|}$
Pembe ya Awamu (Phase Angle) $= \frac{C}{B}$

Kazi uliyopewa ni $y = 6\sin\left(\frac{x}{2} - 90^\circ\right)$ .
Kwa kulinganisha na fomu ya jumla, tunaona:
$A = 6$
$B = \frac{1}{2}$
$C = 90^\circ$

Bainisha thamani ya $B$ .
Kutoka kwa kazi, $B = \frac{1}{2}$ .
Kokotoa kipindi.
$\text{Kipindi} = \frac{360^\circ}{|B|} = \frac{360^\circ}{\left|\frac{1}{2}\right|} = \frac{360^\circ}{\frac{1}{2}} = 360^\circ \times 2 = 720^\circ$
Bainisha thamani ya $C$ .
Kutoka kwa kazi, $C = 90^\circ$ .
Kokotoa pembe ya awamu.
$\text{Pembe ya Awamu} = \frac{C}{B} = \frac{90^\circ}{\frac{1}{2}} = 90^\circ \times 2 = 180^\circ$
Kipindi ni $\boxed{\text{720}^\circ}$ na pembe ya awamu ni $\boxed{\text{180}^\circ}$ .

Determine the period and phase angle for the function y = 6sin(x/2 - 90°).

Answer

Step-by-step solution

Bainisha thamani ya $B$ .

Kokotoa kipindi.

Bainisha thamani ya $C$ .

Kokotoa pembe ya awamu.

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