University:
University of North Georgia
Course:
MATH 1113 | Precalculus
Academic year:

2021
Views:

468

Pages:

2
Author:

Clint W.

Pre-Calculus 5.1 - 5.2 Quiz Review Name: Key Assignment: H4 1. Show that the point (7/25, 24/25) lies on the unit circle. (7/25)² + (24/25)² = 1 49/625 + 576/625 = 1 625/625 = 1 2. The point P is on the unit circle. Find P(x, y) from the given information. a) The y-coordinate is -7/25 and P is in Q4 x² + (-7/25)² = 1 x² + 49/625 = 625/625 x² = 576/625 x = 24/25 or -24/25 (since P is in Q4, x = -24/25) b) The x-coordinate is -2/5; and P lies above the x-axis (-2/5)² + y² = 1 4/25 + y² = 25/25 y² = 21/25 y = √21/5 3. Find the reference angle for the following angles. a) 7π/3 π/3 b) -5π/6 π/6 c) 17π/4 π/4 Find the exact value of the trigonometric function at the given real number. (BY HAND!) 7. sec(11π/6) = 1/cos(11π/6) = 2/√3 = 2√3/3 8. csc(-π) undefined 9. cot(25π/2) cos/sin = 0/1 = 0 10. Find the terminal point on the unit circle determined by the angle. (BY HAND!) a) 3π/2 (0, -1) b) 5π/3 (1/2, -√3/2) c) -3π/4 (-√2/2, -√2/2) 11. 31π/6 (-√3/2, 1/2) 12. -3π (-1, 0) 15. If (-5/13, -12/13) is a terminal point on the unit circle determined by angle θ, then find sinθ, cosθ, and tanθ. sinθ = -12/13 cosθ = -5/13 tanθ = 12/5 Determine the sign of the expression if the terminal point determined by t lies in the given quadrant. 16. tant sect; Q4 (-)(+) = - 17. (cost sect)/(tant); Q2 (-)(-) / (-) = - 18. Given tant > 0 and sint < 0, find the quadrant in which the terminal point of t lies. Q3 Write the first expression in terms of the second if the terminal point determined by t is in the given quadrant. 19. cost, sint; Q4 cos²t = 1 - sin²t cost = √(1 - sin²t) 20. tant, cost; Q3 tan²t = sec²t - 1 tan²t = 1/cos²t - 1 21. Find the values of the five other trigonometric functions if cost = -4/5 and the terminal point determined by t lies in the 3rd quadrant. sint = -3/5 csct = -5/3 tant = 3/4 cott = 4/3 Determine whether the function is even or odd. 22. f(x) = x²cos2x f(-x) = (-x)²cos2(-x) = x²cos2x Even 23. f(x) = sinx + cosx f(-x) = -sinx + cosx Neither