Reading Signs on the Circle
Part of the Trig Equations and Inverses section of Coddy's Trigonometry journey. Lesson 2 of 56.
The special values give sizes: sin(30°) = 1/2, sin(45°) = √2/2 and sin(60°) = √3/2. Cosine takes the same three values in the other order, so cos(30°) = √3/2 and cos(60°) = 1/2. A minus sign does not change the size; it changes where to look.
Take sin(θ) = −√2/2. The size √2/2 gives the reference angle 45°. Sine is the y coordinate, negative below the x axis, in quadrants III and IV. Place 45° in each: 180° + 45°, which is 225°, and 360° − 45°, which is 315°.
Challenge
Tap every angle θ in [0°, 360°) with cos(θ) = −1/2, then press Check.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Trig Equations and Inverses
1Your First Trig Equations
One Equation, Two AnglesReading Signs on the CircleThe Reference AngleRecap: First Equations4Compositions
Draw the TriangleThe Outer FunctionA Negative InsideWhen Undoing Does Not UndoRecap: Compositions2Inverses and Their Ranges
Why arcsin Gives One AngleNegative Inputs to arcsinThe Range of arccosThe Range of arctanRecap: Inverse Ranges5Equations on a Domain
A Negative CosineTangent EquationsEquations in RadiansTwo Turns, Four AnswersRecap: On a Domain