Same Height, Two Angles
Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 3 of 57.
The point at 30° has height one half. In the figure the dashed height is the side opposite 30° in a right triangle whose hypotenuse is the radius, 1, and in a 30-60-90 triangle that side is half the hypotenuse. So sin(30°) = 1/2.
Q is P reflected in the y-axis: same height, opposite across.
Reflect P in the y-axis and you get Q, at 150°. A mirror in the y-axis keeps the height and flips the across, so sin(150°) = 1/2 too. In general θ and 180° - θ have the same sine.
A mirror in the x-axis does the opposite: it keeps the across and flips the sign of the height. The top, sin(90°) = 1, reflects to the bottom, where the height is -1. Two mirrors are all you need to find every angle with a given height.
Challenge
Tap every angle in one turn where the height is minus one half, sin(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 Angles and the Unit Circle
1A Point on a Circle
Height on the CircleAcross: the CosineSame Height, Two AnglesRecap: Height and Across4Radians
What a Radian IsDegrees to RadiansRadians to DegreesRadians Without πTurns in RadiansRecap: Radians5Arc Length and Sector Area
Arc LengthArcs From DegreesFinding the AngleSector AreaRecap: A Slice of Pizza