Problem preview
F-TF.2 Warmup M3-034-A02-V01

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

Find tangent from a point on the unit circle

Problem

If a point on the unit circle is \((1/2,\sqrt{3}/2)\), what is \(\tan(\theta)\)?

Big Picture

What this problem is really about

At a unit-circle point, tangent is vertical over horizontal because it is sine divided by cosine. Check the horizontal coordinate first: a zero denominator makes tangent undefined, while any nonzero value allows the quotient. The coordinate signs also predict the sign of the simplified result and help catch a reversed ratio.

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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 tangent from a point on the unit circle