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. Common #3 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

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. Common #5 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.

10. Common #6 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.

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.