Use the unit-circle diagram to find the terminal point for \(θ~=~5\pi~/4\) and the exact values of \(\sin(θ)\), \(\cos(θ)\), and \(\tan(θ)\).

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The terminal point is (sqrt(2)/2, sqrt(2)/2); sin(theta) = sqrt(2)/2, cos(theta) = sqrt(2)/2, and tan(theta) = 1.

The terminal point is (-sqrt(2)/2, -sqrt(2)/2); sin(theta) = -sqrt(2)/2, cos(theta) = -sqrt(2)/2, and tan(theta) = -1.

The terminal point is (-sqrt(2)/2, sqrt(2)/2); sin(theta) = sqrt(2)/2, cos(theta) = -sqrt(2)/2, and tan(theta) = -1.

The terminal point is (-sqrt(2)/2, -sqrt(2)/2); sin(theta) = -sqrt(2)/2, cos(theta) = -sqrt(2)/2, and tan(theta) = 1.

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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: Find exact sine, cosine, and tangent from a special-angle point