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 ∅