Math Problem Statement

Solve trigonometric equations and analyze cosine graphs.

Solution

The images show cosine graphs and trigonometric equations with missing values to be filled in.

  1. Cosine Graphs:

    • Both images display the graph of y=cosxy = \cos x.
    • The second graph appears slightly different in amplitude and alignment compared to the first.
    • The graphs extend from 360-360^\circ to 360360^\circ.
  2. Trigonometric Equations:

    • The third image consists of sine and cosine equations with solutions to be completed.
    • The provided answers include angles such as 48,132,283,32,328,331,48^\circ, 132^\circ, 283^\circ, 32^\circ, 328^\circ, 331^\circ, and 151-151^\circ.
    • 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:

  1. How do you determine the reference angles for sine and cosine equations?
  2. Why does the cosine graph appear different in both images?
  3. What are the general solutions for sinx=k\sin x = k and cosx=k\cos x = k?
  4. How can you solve trigonometric equations using the unit circle?
  5. How does the period of cosine affect the graph?

Tip:

When solving sinx=k\sin x = k or cosx=k\cos x = k, 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