Trigonometric identities-solving triangles

Question

Questions:

Trigonometric Identities, Solving Triangles, Focus, Directrix, Sequences , Sums and Derivatives

1. Complete the identity. cos² sinq/cosq + cosq/sinq = ?
a. sin q tan q
b. -2 tan 2q
c. 1+cot q
d. sec q + csc q

2. Complete the identity. Sin(a+b) cos b - cos(a+b) sin b
a. sin a
b. sin a b-sin a b
c. 2 sin b cos b(sin a - cos a)
d. sin a cos b - cos a sin b

3. Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.

            A = 23^o, B = 21^o, a = 42.8

a. C = 137^o, b = 76.1, c = 39.3
b. C = 137^o, b = 39.3, c = 76.1
c. C = 136^o, b = 39.3, c = 76.1
d. C = 137^o, b = 76.1, c = 39.3

4. Solve the problem; The distance from home plate to dead center field in Sun Devil Stadium is 401 feet. A baseball diamond is a square with a distance from home plate to first base of 90 feet. How far is it from first base to dead center field?
a. 326.2 feet
b. 343.3 feet
c. 469 feet
d. 390.8 feet

5. Find the focus and directrix of the parabola with the given equation.

               y² = -32x

a. focus (8,0) diractrix x=-8
b. focus (-8,0) diractrix x=8
c. focus (0,-8) diractrix x=8
d. focus (-8,0) diractrix x=8

6. Write the first five terms of the sequence whose general term is given.
                       a_n= 4(2n - 3) n = 1,2,3...
a. -4,4,12,20,28
b. -4,-8,-12,-16,-20
c. -1,1,3,5,7
d. -12,-4,4,12,20

7. Find the indicated sum;Σ⁴_i-1 1/7i
a. 1/28
b. 25/84
c. 11/42
d. 5/28

8. Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be applied.

              lim_x→1 3x² + 7x -2/3x² - 4x + 2

a. Does not exist
b. - 7/4
c. 8
d. 0

9. Find the derivative of f at x. That is, find f(x)'

           ƒ(x) = x² - 8x - 17 at x = 4

a. -8
b. 8
c. 0
d. -6