Trigonometry Mastered

Explore the most graphing calculator tool, learn to graph functions, compare online and offline modes, and use derivatives, integrals, and parlor graphing features, plus apps and teaching resources.

the unit circle at the origin with radius one is described by x^2 + y^2 = 1, and you can shift circles using (x-h)^2+(y-k)^2=r^2 while testing points.

Master terminal points on the unit circle by traveling from (1,0) ccw or cw to angles like pi/6, pi/3, and pi/4, obtaining coordinates such as (0,1) and (±1/√2, ±1/√2).

Learn to graph sine and cosine using the unit circle, with attention to x and y components and their cycles. Derive amplitude and period from coefficients and recognize periodic behavior.

Identify reference angles as the smallest angle between the terminal side and the x axis, and use them to determine sine and cosine values for various angles.

Explore how inverse trigonometric functions arise from inverse functions by restricting sine, cosine, and tangent to specific domains. Learn the corresponding arcsine, arccosine, and arctangent with their domains and ranges.

Learn to rewrite a sin x + b cos x as k sin(x+phi) with k = sqrt(a^2+b^2) and cos phi = a/k, sin phi = b/k; see examples.

Master double angle formulas for sin 2x, cos 2x, and tan 2x, including sin 2x = 2 sin x cos x and cos 2x = 2 cos^2 x - 1.

Learn and apply half-angle formulas for sine, cosine, and tangent, including plus/minus signs by quadrant, with worked examples like sin(pi/8) and cos(105 degrees) to solve problems.

Explore converting polar and rectangular equations using x = r cos theta and y = r sin theta, derive r^2 = x^2 + y^2, and tan theta = y/x.

Explore polar curves: circles from r = a, circles shifted by sine or cosine, spirals, limacons (cardioid and inner loop), and rose curves r = a sin(nθ) or a cos(nθ).

Master multiplying and dividing complex numbers in polar form by multiplying the modules and adding the arguments, or dividing the modules and subtracting the arguments, using cosign and sign components.