Problem preview
F-TF.2 Warmup M3-034-A13-V01

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

Find the missing sine or cosine value from a given unit-circle coordinate and quadrant

Problem

If \(\sin(\theta)~=~3/5\) and \(\theta\) is in \(\text{Quadrant}~I\), what is \(\cos(\theta)\)?

Big Picture

What this problem is really about

The unit-circle identity recovers the magnitude of a missing coordinate, but squaring erases its sign. Solve for the squared coordinate, take both algebraic roots, and then use the quadrant to keep the geometrically valid sign. Substituting both coordinates back into the identity provides a clean check.

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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
Find the missing sine or cosine value from a given unit-circle coordinate and quadrant