TRIGONOMETRY COSθ WITH 360° VALUE WORKING MODEL

TRIGONOMETRY COSθ WITH 360° VALUE WORKING MODEL

In trigonometry, the cosine function (cos) represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. Like the sine function, the cosine function is periodic with a period of 360 degrees (or 2π radians). Let’s explore how cos(θ) varies with different angles within a 360-degree cycle:

1. Understanding the Cosine Function:

• The cosine function is defined as cos(θ) = Adjacent / Hypotenuse.
• In a unit circle (circle with radius 1), the cosine of an angle θ is equal to the x-coordinate of the point where the terminal side of the angle intersects the unit circle.

2. Graphing the Cosine Function:

• When graphed, the cosine function produces a wave-like pattern that oscillates between -1 and 1 as the angle θ increases from 0 to 360 degrees (or 0 to 2π radians).
• At θ = 0° (or 0 radians), cos(0) = 1, and the function starts at its maximum value.
• As θ increases, cos(θ) oscillates between its maximum value of 1 (at θ = 0° or 0 radians) and its minimum value of -1 (at θ = 180° or π radians).
• At θ = 360° (or 2π radians), cos(θ) returns to its maximum value of 1, completing one full cycle.

3. Using Trigonometric Values:

• Trigonometric tables or calculators can provide the cosine values for specific angles within the 360-degree cycle.
• For example, cos(30°) = √3 / 2, cos(45°) = √2 / 2, cos(60°) = 0.5, cos(90°) = 0, and so on.

4. Applications:

• The cosine function is used in various fields, including geometry, physics, engineering, and astronomy.
• It describes phenomena such as periodic motion, oscillations, waves, and alternating current.

In summary, the cosine function (cos) represents the ratio of the adjacent side to the hypotenuse in a right triangle, and it varies periodically with angles within a 360-degree cycle. Understanding the behavior of cos(θ) with different angles is fundamental in trigonometry and has practical applications in various fields.

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