Determine magnitude and direction of resultant force

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Reference no: EM13544550

1. Use your calculator and calculate the value of the following, write your answer in fractions.

a) tan 60o - tan 30o/1 + tan30o.tan60o

b) 5 tan 60° -3 sin 60°

2. Solve the following triangle.

1964_Calculate the area of the triangle.png

3. Solve the following triangle and calculate the area of the triangle.

156_Calculate the area of the triangle1.png

4. Evaluate the following

(a) secant 5.37 (b) cosecant

(c) cotangent Π/24

5. Evaluate the following trignomentric functions

(s) sec-1 2.3164 (b) cosec-1 1.1784

(c) cot-1 2.1273

6. In a triangle XYZ, ?X = 51°, ?Y=67° and YZ=15.2 cm. Solve the triangle and find its area. (Apply sine or cosine rule accordingly)

7. Sole the follwing triangle and find the area of the triangle.

1131_Calculate the area of the triangle2.png

8. Prove the following identities

a) cos²x tan²x + cos²x = 1

b) 1 + cotθ/1 + tanθ = cotθ

c) 1/cos2x - 1/cot2x - 1/cosec2x = cos2x

9. Expand 

(x³-x+1) (x³-2x²-1)

10. Factorise the following

a) 5x²y - 10ax² + 5x²

b) X(2a-y) + 3b(2a-y)

c) K(2x-1) - m(1-2x)

d) 16a² - 25b²c²

e) t² - t - 6

f) 2x² - 5x + 3

11. Simplify sin (45° + ?) - sin (45° - ?)

12. Factorise where possible and simplify

(3x² - 7x + 4) / (x² - 1)

13. Given that the roots/solutions of the quadratic equation ax2+ bx + c =0 are x1,2 = -b ± √(b2 -4ac)/2a, solve the equation below, giving the roots correct to three significant figures: -4y2 + 3y + 2 = 0.

14. Solve the following

(2t - 1)/ 3 = (9 - 2t) / 6t

15. Evaluate the following

(a) log3 9 (b) log10 10 (c) log16 8

16. Simplify the following

a) Log 4 + log 0.25

b) Log 3 - log 2 - log 6

c) Log2 100

17. Solve the following exponential functions using logarithms

a)4(3-x) = 2√2

18. Given that

M - 5t = 3

-2m + 4t = -1

Evaluate  using determinent method a)Δ b) Δ m c) Δt

19. Write each of the following in the form a log x + b log y + . . . 

a) log P/Qn

b) log (xy)n

20. Find the product of the two matrices given below

583_Calculate the area of the triangle3.png

21.                         

704_Calculate the area of the triangle4.png

Write down the matrix A.

22. For the system of forces acting at a point, determine the magnitude and direction of the resultant force.

572_Calculate the area of the triangle5.png

23. Expand (i.e. multiply out):

a) 4n-2/3(n-2n-1/2)

b) (et + e-t)(et - e-t)

24. Multiply and divide out, expressing in simplest exponential form:

a) e-x - ex/ex

b) 2x1/2(3x-1/2 - 6x0)/3x

25. Draw the graph for the following sine function. (Use the graph sheet attached)

                                       Y = 5 cos (½) x - 3

Reference no: EM13544550

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