Algebra III Chapter 7

12. Use a half-angle identity to find the exact value of cos 165°

-½ √2+√3

4. Simplify ((cos x)/(sec x - 1)) + ((cos x)/(sec x +1))

2 cot² x

9. Which expression is not equivalent to cos 2∅? A. cos² ∅ - sin² ∅ B. 2 cos² ∅ -1 C. 1 - 2 sin² ∅ D. 2 sin ∅ cos ∅

2 sin ∅ cos ∅

11. If csc ∅ = -5/3 and ∅ has its terminal side in Quadrant III, find the exact value of tan 2∅

24/7

2. If csc∅ = -5/4 and 180°<∅<270°, find tan∅

4/3

14. Solve 2 cos² x - 5 cos x + 2 = 0 for principle values of x

60°

1. Find an expression equivalent to (sec∅ tan∅)/sin∅

sec²∅

5. Find a numerical value of one trigonometric function of x if ((tan x)/(cot x)) - ((sec x)/(cos x)) = 2/(csc x)

sin x = 1/2

17. Write the standard form of the equation of a line for which the length of the normal is 6 and the normal makes an angle of 120° with the positive x-axis

x - √3 y + 12 = 0

13. Solve 4 sin² x + 4√2 cos x - 6 = 0 for all real values of x

π/4 + 2πk, (7π)/4 + 2πk

19. Find the distance between the lines with equations 3x - y = 9 and y = 3x -4

√10 / 2

16. Write the equation 2x + 3y - 5 = 0 in normal form

((2√13)/13)x + ((3√13)/13)y - ((5√13)/13) = 0

3. Simplify (tan²∅ csc²∅ - 1)/tan²∅

1

6. Use a sum or difference identity to find the exact value of sin 255°

(-√2 - √6)/4

18. Find the distance between P(-4,3) and the line with equation 2x - 5y = 7

(16√29)/29

20. Find an equation of the line that bisects the obtuse angles formed by the lines with equations 3x - y = 1 and x + y = -2

(3√2 - √10) x - (√10 + √2) y - 2√10 - √2 = 0

15. Solve 2 sin x + √3 < 0 for 0≤x<2π

(4π)/3 < x < (5π)/3

10. If cos ∅ = 0.8 and 270°<∅<360°, find the exact value of sin 2∅

-0.96

7. Find the value of tan (α - β) if cos α = -3/5, sin β = 5/13, 90°<β<180°

-33/56

8. Which expression is equivalent to cos (π-∅)? A. -cos ∅ B. cos ∅ C. -sin ∅ D. sin ∅

-cos ∅