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Basic Trig Identities sin^2 (x) + cos ^2 (x) = 1

Basic Trig Identities sin^2 (x) + cos ^2 (x) = 1 sin(-x) = -sin(x) , cos(-x) = cos(x) , tan(-x) = -tan(x) sin(x + 2Pi) = sin(x), cos(x + 2*Pi) = cos(x), tan(x + Pi) = tan(x) Special values: sin(Pi/3) = sqrt(3)/2 cos(Pi/3) = 1/2 sin(Pi/6) =1/2 cos(Pi/6) = sqrt(3)/2

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Basic Trig Identities sin^2 (x) + cos ^2 (x) = 1

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  1. Basic Trig Identities sin^2 (x) + cos ^2 (x) = 1 sin(-x) = -sin(x) , cos(-x) = cos(x) , tan(-x) = -tan(x) sin(x + 2Pi) = sin(x), cos(x + 2*Pi) = cos(x), tan(x + Pi) = tan(x) Special values: sin(Pi/3) = sqrt(3)/2 cos(Pi/3) = 1/2 sin(Pi/6) =1/2 cos(Pi/6) = sqrt(3)/2 sin(Pi/4) = sqrt(2)/2 = cos(Pi/4)

  2. Addition formulae sin(x + y) = sin(x)cos(y) + sin(y)cos(x) cos(x + y) = cos(x)cos(y) – sin(x)sin(y) sin(x - y) = sin(x)cos(y) - sin(y)cos(x) cos(x - y) = cos(x)cos(y) + sin(x)sin(y)

  3. Double angle and half angle formulae sin( 2x) = 2sin(x)cos(x) cos(2x) = cos^2(x) - sin^2(x) cos(x/2) = sqrt((1+cos(x))/2) sin(x/2) = sin(x)/cos(x/2)

  4. In a triangle ABC with the sides opposite the angles labelled a, b, and c respectively: Law of cosines: c^2 = a^2 + b^2 – 2ab cos(C) Law of sines: a/sin(A) = b/sin(B) = c/sin(C)

  5. Common #1 In the triangle ABC the edge AB has length 18 inches and the edge BC has length 15 inches. The angle ABC measures .590 radians. The length of the line AC is ___ inches and the angle BAC measures _____ radians.

  6. Common #2 Complete the following table. Each row and colum contains the sine and cosine of angles a and b. Enter sin(a-b) at the intersection of the row and column. sin(a-b) sin(a) = .422, cos(a) = -.906 sin(b)= .839 cos(b)=-.545

  7. In the triangle in the diagram the tangent of the angle BAC is OPP/adj = t/q and the sine of the angle BAC is opp/hyp = t/u Common #3

  8. Common # 4 Use your calculator to answer the following. The angle BAC in the diagram measures   ___ radians or  ___degrees. First box: arctan(7/8) = .7188 radians Second box: .7188*180/Pi = 41.184 degrees

  9. The radius of the circle in the diagram is 22 cm. and the length of the arc from A to B is 29.950 cm. The length of the  chord AB is  ________cm. Common #5

  10. As indicated in the diagram (which is not to scale) the tangent line to the graph of f(x) = -x^2-3x-90 at x = 6 meets the x-axis at an angle AOB whose tangent is _______ . The angle AOB measures  _______radians. Common #6

  11. Common # 9 If sin(a) = .891, cos(a) = .454 and sin(b) = .766, cos(b) = -.643 Then cos(a+b) =

  12. Common #11 From a distance of 1644 feet the top of a tower subtends an angle of 41.2352 degrees. Within 2 feet the height of the tower is  _______feet.

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