Math  /  Trigonometry

QuestionWhat is the amplitude and period of the given graph. Every mark or 3/43 / 4 pi, pi, 5/4pi etc. The period is integral or fractional. e.g. pi, 3pi,8pi,1/2pi,3/4pi,1/3r3 \mathrm{pi}, 8 \mathrm{pi}, 1 / 2 \mathrm{pi}, 3 / 4 \mathrm{pi}, 1 / 3 \mathrm{r} Write pi for π\pi

Studdy Solution

STEP 1

What is this asking? Find out how tall the wave is and how long it takes to repeat! Watch out! Don't confuse the amplitude with the maximum value, and remember the period is the length of one complete cycle!

STEP 2

1. Determine the amplitude
2. Determine the period

STEP 3

First, let's **understand what amplitude means**.
It's the height from the middle of the wave to the top or bottom.
So, it's half the distance between the maximum and minimum values.

STEP 4

The maximum value of our graph is **2** and the minimum value is **-2**.
So, the total height of the wave is:
2(2)=42 - (-2) = 4

STEP 5

Now, let's **find the amplitude** by dividing this total height by 2:
Amplitude=42=2\text{Amplitude} = \frac{4}{2} = 2

STEP 6

The **period** is the length of one complete cycle of the wave.
From the description, the graph completes one full cycle between 00 and 2π2\pi.

STEP 7

So, the **period** of the graph is:
2π2\pi

STEP 8

The amplitude of the graph is **2**, and the period is **2π2\pi**.

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