Calculate the area of the triangle - exponential functions

Question

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

a) tan 60^o - tan 30^o/1 + tan30^o.tan60^o

b) 5 tan 60° -3 sin 60°

2. Solve the following triangle.

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

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.

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

21.                         

Write down the matrix A.

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

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

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

b) (e^t + e^-t)(e^t - e^-t)

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

a) e^-x - e^x/e^x

b) 2x^1/2(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