Use the unit-circle diagram to evaluate \(\cos(5\pi~/4)\). Give the exact value, its decimal value, and the result rounded to \(\text{four}~\text{decimal}~\text{places}\).

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The exact value is -sqrt(2)/2; its decimal value is -0.7071067811..., which rounds to -0.7070 to four decimal places.

The exact value is -1/2; its decimal value is -0.5, which rounds to -0.5000 to four decimal places.

The exact value is sqrt(2)/2; its decimal value is 0.7071067811..., which rounds to 0.7071 to four decimal places.

The exact value is -sqrt(2)/2; its decimal value is -0.7071067811865476..., which rounds to -0.7071 to four decimal places.

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Curriculum context

Course: Math III
Standard: F-TF.2
Category: Functions
Domain: Trigonometric Functions
Objective: Use the unit circle to extend trig functions to all real-number radian measures.
Problem type: Report exact and four-decimal unit-circle values