Problem preview
F-TF.2 Warmup M3-034-A03-V01

Use the unit circle to extend trig functions to all real-number radian measures.

Select sine, cosine, and tangent signs by quadrant

Problem

A terminal point \((x,~y)\) lies strictly inside \(\text{Quadrant}~I\) on the unit circle. Use the diagram to determine the signs of \(\sin(θ)\), \(\cos(θ)\), and \(\tan(θ)\), and verify them from the signs of \(x\), \(y\), and \(y/x\).

Big Picture

What this problem is really about

Trig signs come directly from terminal-point coordinates rather than from a separate rule to memorize. Cosine follows the horizontal coordinate, sine follows the vertical coordinate, and tangent follows their quotient. Because the point lies strictly inside a quadrant, neither coordinate is zero, so the tangent sign is determined normally.

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Four variants of this problem type
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
Select sine, cosine, and tangent signs by quadrant