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TRIGONOMETRY

TRIGONOMETRY. By Mindy Crall. 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

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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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