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7 Course 7 of 10

Trigonometry

Sine, cosine and tangent start on the unit circle and end up measuring things you can't reach: the height of a building, the distance to a boat, the shape of a sound wave. Every lesson has examples worked step by step, practice problems with solutions and a quick check at the end.

Before you start: Algebra 2, geometry (especially special right triangles and similarity) and some coordinate geometry.

Lessons
11
Units
4
Reading
2.3 h
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Unit 1 Trig functions

  1. 1 Angles in standard position and radian measure Angles as rotations, standard position, coterminal angles, radian measure, converting between degrees and radians, and arc length. 11 min
  2. 2 Sine and cosine on the unit circle The unit circle, defining sine and cosine for any angle, the Pythagorean identity, signs in each quadrant and values at the quadrantal angles. 12 min
  3. 3 Tangent and the reciprocal functions The tangent function, its connection to slope, the reciprocal functions secant, cosecant and cotangent, and finding all six values from one. 11 min
  4. 4 Special angles and reference angles Exact trig values for 30, 45 and 60 degrees, and how reference angles let you evaluate trig functions of any angle without a calculator. 12 min
  5. 5 Graphing sine, cosine and tangent The graphs of sine, cosine and tangent, and how amplitude, period, phase shift and vertical shift transform them. 13 min

Unit 2 Identities

  1. 6 Sum, difference and double-angle identities The sum and difference identities for sine, cosine and tangent, the double-angle and half-angle identities, and using them for exact values and proofs. 13 min

Unit 3 Equations and inequalities

  1. 7 Inverse trig functions and basic equations Arcsine, arccosine and arctangent with their restricted ranges, and how to find every solution of sin x = a, cos x = a and tan x = a. 13 min
  2. 8 Solving trigonometric equations Solving trig equations by isolating, factoring, treating them as quadratics, using identities, and handling multiple angles. 13 min
  3. 9 Trigonometric inequalities Solving inequalities like sin x > a and cos x ≤ a using the unit circle or the graph, on one period or for all real numbers. 11 min

Unit 4 Solving triangles

  1. 10 Right triangle trigonometry SOH-CAH-TOA, solving right triangles, finding angles with inverse functions, and angles of elevation and depression in real-world problems. 13 min
  2. 11 The law of sines, the law of cosines and triangle area Solving any triangle with the law of sines and the law of cosines, the ambiguous SSA case, and the area formula using sine. 14 min