Math Problem Statement
Solution
The images show cosine graphs and trigonometric equations with missing values to be filled in.
-
Cosine Graphs:
- Both images display the graph of .
- The second graph appears slightly different in amplitude and alignment compared to the first.
- The graphs extend from to .
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Trigonometric Equations:
- The third image consists of sine and cosine equations with solutions to be completed.
- The provided answers include angles such as and .
- The missing values should be determined using trigonometric identities and reference angles.
Would you like a detailed step-by-step solution for filling in the missing values?
Related Questions:
- How do you determine the reference angles for sine and cosine equations?
- Why does the cosine graph appear different in both images?
- What are the general solutions for and ?
- How can you solve trigonometric equations using the unit circle?
- How does the period of cosine affect the graph?
Tip:
When solving or , always consider the reference angle and the quadrants where the function is positive or negative.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Graphs of Trigonometric Functions
Solving Trigonometric Equations
Formulas
y = cos(x)
sin(x) = k → x = arcsin(k) + 360°n, x = 180° - arcsin(k) + 360°n
cos(x) = k → x = arccos(k) + 360°n, x = -arccos(k) + 360°n
Theorems
Unit Circle
Reference Angles
Quadrant Rules
Suitable Grade Level
Grades 9-12
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