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TRIGONOMETRY

Explore fundamental trigonometric concepts like angles, conversions between degrees and radians, right triangle trigonometry definitions, special right triangles, basic trigonometric identities, graphing sine and cosine functions, and more. Understand coterminal angles, trigonometric identities, and the laws of sines and cosines.

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TRIGONOMETRY

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  1. TRIGONOMETRY By Mindy Crall

  2. Angles, Arc length, Conversions Angle measured in standard position. Initial side is the positive x – axis which is fixed. Terminal side is the ray in quadrant II, which is free to rotate about the origin. Counterclockwise rotation is positive, clockwise rotation is negative. Coterminal Angles: Angles that have the same terminal side. 60°, 420°, and –300° are all coterminal. Degrees to radians: Multiply angle by Radians to degrees: Multiply angle by Note: 1 revolution = 360° = 2π radians.

  3. Right Triangle Trig Definitions B • sin(A) = sine of A = opposite / hypotenuse = a/c • cos(A) = cosine of A = adjacent / hypotenuse = b/c • tan(A) = tangent of A = opposite / adjacent = a/b • csc(A) = cosecant of A = hypotenuse / opposite = c/a • sec(A) = secant of A = hypotenuse / adjacent = c/b • cot(A) = cotangent of A = adjacent / opposite = b/a c a A C b

  4. Special Right Triangles 30° 45° 2 1 60° 45° 1 1

  5. Basic Trigonometric Identities Quotient identities: Even/Odd identities: Even functions Odd functions Odd functions Reciprocal Identities: Pythagorean Identities:

  6. All Students Take Calculus. Quad I cos(A)>0 sin(A)>0 tan(A)>0 sec(A)>0 csc(A)>0 cot(A)>0 cos(A)<0 sin(A)>0 tan(A)<0 sec(A)<0 csc(A)>0 cot(A)<0 Quad II cos(A)<0 sin(A)<0 tan(A)>0 sec(A)<0 csc(A)<0 cot(A)>0 cos(A)>0 sin(A)<0 tan(A)<0 sec(A)>0 csc(A)<0 cot(A)<0 Quad IV Quad III

  7. Graphs of sine & cosine

  8. Sine graphs y = sin(x) y = sin(x) + 3 y = 3sin(3x-9)+3 y = sin(x) y = sin(3x) y = sin(x/3) y = sin(x – 3) y = 3sin(x)

  9. Graphs of cosine y = cos(x) y = 3cos(x) y = cos(x) + 3 y = cos(3x) y = cos(x – 3) y = 3cos(3x – 9) + 3 y = cos(x) y = cos(x/3)

  10. Tangent and cotangent graphs

  11. Graphs of tangent and cotangent y = tan(x) y = cot(x)

  12. Graphs of secant and cosecant y = sec(x) y = cos(x) y = csc(x) y = sin(x)

  13. Trigonometric IdentitiesSummation & Difference Formulas

  14. Trigonometric IdentitiesDouble Angle Formulas

  15. Law of Sines & Law of Cosines Law of sines Law of cosines Use when you haveSSA. Use when you have SAS, SSS.

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