How do I apply the period of my COsin equation? Also how do I know what what to put in the x values?
I'm mostly confused about what I need to put in the x values. I'm aware the values of x are from the angle radians and stuff. This has been bothering me for so long
Transcribed Image Text:**Transcription and Explanation for Educational Website**
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**Title: Understanding Trigonometric Graphs**
**Instructions and Notes:**
1. **Graph the Function y = (3 cos(2x + π/2)):**
- **Graph Features:**
- **Amplitude (amp):** 3
- **Period:** \( \text{Periodic Interval } = \frac{2\pi}{2} = \pi \)
- **Steps to Graph:**
1. Use the unit circle to determine key features.
2. Identify key points over a two-period interval, starting from \( -3\pi \) to \( 3\pi \).
3. Note reflection over the x-axis.
- **Graph Characteristics:**
- The cosine function has been modified to have an amplitude of 3, and the period has been altered to \( \pi \).
2. **Determine an Equation for Form y = a * sin(bx):**
- **Task:**
- Determine the equation based on the graph provided.
- Analyze amplitude and period from visual graph features.
**Graph Explanations:**
- The graph of \( y = 3 \cos(2x + \pi/2) \) has been plotted. The amplitude of 3 means that the graph will achieve maximum and minimum values of 3 and -3, respectively.
- **Additional Notes:**
- Reflection properties are indicated by changes in the direction of the graph concerning the x-axis. These are seen as the function values move from 3 to -3 and vice versa.
- The periodic interval information instructs on how frequently the cosine function repeats, based on altering its usual \( 2\pi \) period to \( \pi \).
**Conceptual Points:**
- **Amplitude Changes** impact the height of the wave from the equilibrium line.
- **Period Adjustments** (via 'b') affect how compressed or stretched the wave appears over the x-axis.
**Further Study Directions:**
- Practice plotting both sine and cosine functions with varying amplitudes and frequencies.
- Explore how horizontal and vertical shifts affect positioning and symmetry.
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This lesson reinforces understanding of trigonometric transformations, a crucial concept in algebra and pre-calculus.
Figure in plane geometry formed by two rays or lines that share a common endpoint, called the vertex. The angle is measured in degrees using a protractor. The different types of angles are acute, obtuse, right, straight, and reflex.
