Problem preview
F-TF.2 Warmup M3-034-A01-V01

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

Find cos(θ) and sin(θ) from a point on the unit circle

Problem

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

Big Picture

What this problem is really about

A unit-circle terminal point stores the two basic trig values in coordinate order: cosine is horizontal and sine is vertical. Preserve that order before reading signs or magnitudes. Squaring and adding the two coordinates should give one, which checks that the point and the resulting values are consistent with the unit circle.

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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 cos(θ) and sin(θ) from a point on the unit circle