Makati Science High School 4th Quarter Periodical Test on Trigonometry 2018-2019 PDF

Makati Science High School Kalayaan Avenue, Barangay Cembo, Makati City 4^th^ Quarter Periodical Test on Trigonometry SY 2018-2019 Name: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ Date: \_\_\_\_\_\_\_\_\_\_\_\_\_\_ Score:\_\_\_\_\_\_\_\_\_\_ Section...

Makati Science High School Kalayaan Avenue, Barangay Cembo, Makati City 4^th^ Quarter Periodical Test on Trigonometry SY 2018-2019 Name: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ Date: \_\_\_\_\_\_\_\_\_\_\_\_\_\_ Score:\_\_\_\_\_\_\_\_\_\_ Section: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_Parent's Signature: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ **DIRECTIONS**: Read each item carefully. Write the letter of the best answer on the space before each number. Use CAPITAL LETTERS. 1. What property of the graph of the trigonometric function refers to the distance it takes for the graph to complete one complete cycle? A. Period B. Amplitude C. Phase shift D. Vertical Shift 2. What property of the graph of the trigonometric function refers to the maximum or the minimum value of the graph from the "resting" position? A. Period B. Amplitude C. Phase shift D. Vertical Shift 3. Which of the following is/are TRUE for the graph of [*y* = sin *x*]{.math.inline}? I. Domain: all real numbers II. Range: [ − 1 ≤ *y* ≤ 1]{.math.inline} III. Period: [2*π*]{.math.inline} A. Only I B. Only II C. Only III D. all of the above 4. What is the period of [*y* = 2cos 4*x*]{.math.inline}? A. [\$\\frac{\\pi}{2}\$]{.math.inline} B. [*π*]{.math.inline} C. [8*π*]{.math.inline} D. [4*π*]{.math.inline} 5. The function [*y* = csc *x*]{.math.inline} is NOT defined at [*x*]{.math.inline} equals to A. [\$- \\frac{\\pi}{4}\$]{.math.inline} B. [\$\\frac{\\pi}{2}\$]{.math.inline} C. [\$- \\frac{\\pi}{2}\$]{.math.inline} D. [*π*]{.math.inline} 6. If [tan *x* = 1, *x* ]{.math.inline}not in QI, which of the following is TRUE? I. [\$\\sin\\text{x\\ } = - \\frac{\\sqrt{2}}{2}\$]{.math.inline} II. [\$\\cos\\text{x\\ } = - \\frac{\\sqrt{2}}{2}\$]{.math.inline} III. [cot x  = 1]{.math.inline} A. Only I B. Only II C. Only III D. all of the above 7. The graph of [*y* =  − tan *x*]{.math.inline} has an asymptote at A. [*x* = 0]{.math.inline} B. [\$x = \\frac{\\pi}{4}\$]{.math.inline} C. [\$x = \\frac{\\pi}{2}\$]{.math.inline} D. [*x* = *π*]{.math.inline} 8. The function whose graph appears below has an equation of A. [*y* = 2sin *x*]{.math.inline} B. [*y* =  − 2sin *x*]{.math.inline} C. [ *y* = 2cos *x*]{.math.inline} D. [*y* = cos 2*x*]{.math.inline} 9. If [\$\\text{Arcsin}x = - \\frac{1}{2}\$]{.math.inline}, then [*x*=]{.math.inline} A. [\$\\frac{\\pi}{6}\$]{.math.inline} B. [\$\\frac{\\pi}{3}\$]{.math.inline} C. [\$- \\frac{\\pi}{6}\$]{.math.inline} D. [\$- \\frac{\\pi}{3}\$]{.math.inline} 10. For what value of [*x*]{.math.inline} will make the equation [cos *x* + sin *x* = 1]{.math.inline}? A. [*x* = 0]{.math.inline} B. [\$x = \\frac{\\pi}{4}\$]{.math.inline} C. [*x* = *π*]{.math.inline} D. [*x* ∈ ℝ]{.math.inline} 11. Simplify: [tan (Arcsin1)]{.math.inline} A. 0 B. 1 C. [ − 1]{.math.inline} D. undefined 12. In the general form of the function [*y* = acos*b*(*x*−*c*) + *d*]{.math.inline}, which parameter will affect the period of the graph of the function? A. a B. b C. c D. d 13. Which of the following is an equation of a sine curve with maximum value 8 and minimum value 2, and period [8*π*]{.math.inline}? A. [\$y = 3\\sin{\\frac{x}{4} + 5}\$]{.math.inline} B. [\$y = 8\\sin{\\frac{x}{4} - 2}\$]{.math.inline} C. [\$y = 3\\sin{\\frac{x}{8} + 5}\$]{.math.inline} D. [\$y = 6\\sin{\\frac{x}{4} + 2}\$]{.math.inline} 14. What is the domain of the cosine function? A. [\[0, ∞)]{.math.inline} B. all real numbers C. [( − ∞, 0\]]{.math.inline} D. [\[ − 1, 1\]]{.math.inline} 15. What is the minimum value of [*y* = sin *x* + 1]{.math.inline}? A. 0 B. 1 C. 2 D. 3 16. What is the period of [\$y = \\frac{3}{2}\\sin{4x - 7}\$]{.math.inline}? A. {.math.inline} B. [\$\\frac{\\pi}{2}\$]{.math.inline} C. [*π*]{.math.inline} D. [2*π*]{.math.inline} 17. The function [*y* = tan *x*]{.math.inline} is NOT defined at [*x*]{.math.inline} equals to? A. {.math.inline} B. [\$\\frac{\\pi}{2}\$]{.math.inline} C. [ − *π*]{.math.inline} D. [2*π*]{.math.inline} 18. What is the range of the [*y* = tan^ − 1^*x*]{.math.inline}? A. [\[ − 1, 1\]]{.math.inline} B. all real numbers C. [( − ∞, 0\]]{.math.inline} D. [\$\\left\\{ y\\mathbb{\\in R,\\ }x \\neq \\frac{\\pi}{2} + 2n\\pi \\right\\}\$]{.math.inline} 19. If [sec *x* = 2, *x* ]{.math.inline}not in Q4, which of the following is true? I. [\$\\csc\\text{x\\ } = - \\frac{2\\sqrt{3}}{3}\$]{.math.inline} II. [\$\\tan\\text{x\\ } = - \\frac{\\sqrt{3}}{3}\$]{.math.inline} III. [cot x  = 3]{.math.inline} A. Only I B. Only II C. Only III D. none of the above 20. If the sine function [*y* =  − 4sin bx]{.math.inline} has a period [6*π*]{.math.inline}, then what could be the value of b? A. {.math.inline} B. [\$\\frac{1}{2}\$]{.math.inline} C. [\$\\frac{1}{3}\$]{.math.inline} D. [\$\\frac{1}{4}\$]{.math.inline} 21. Which of the following sine function will NOT pass through the origin? A. [*y* =  − 2sin 3*x*]{.math.inline} C. [*y* = 2sin (*x* + *π*)]{.math.inline} B. [*y* = 3sin 2*x*]{.math.inline} D. [\$y = 2\\sin\\left( x - \\frac{\\pi}{3} \\right)\$]{.math.inline} 22. What the value of [\$\\text{Arccos}\\left( - \\frac{1}{2} \\right)\$]{.math.inline}? A. [\$\\frac{5\\pi}{6}\$]{.math.inline} B. [\$\\frac{2\\pi}{3}\$]{.math.inline} C. [\$- \\frac{5\\pi}{6}\$]{.math.inline} D. [\$- \\frac{2\\pi}{3}\$]{.math.inline} 23. What is the phase shift of [*y* = sin (2*x* + *π*) − 2]{.math.inline}? A. [\$\\frac{\\pi}{2}\$]{.math.inline} to the left B. [\$\\frac{\\pi}{2}\$]{.math.inline} to the right C. [*π*]{.math.inline} to the left D. [*π*]{.math.inline} to the right 24. What is the domain of the function, [*y* = arctan *x*]{.math.inline}? A. [\$x = \\frac{\\pi}{2} + k\\pi,\\ \\text{where}\\text{\\ k\\ }\\text{is\\ an\\ integer}\$]{.math.inline} C. [\$x = \\frac{\\text{kπ}}{2},\\ \\text{where}\\text{\\ k\\ }\\text{is\\ an\\ integer}\$]{.math.inline} B. [{*x* ∈ ℝ}]{.math.inline} D. [*x* = 2*π* + *kπ*, where k is an integer]{.math.inline} 25. Which of the following is equal to [Arctan( − 1)]{.math.inline}? A. [\$\\frac{3\\pi}{4}\$]{.math.inline} B. [\$\\frac{7\\pi}{4}\$]{.math.inline} C. [\$\\frac{5\\pi}{4}\$]{.math.inline} D. [\$- \\frac{3\\pi}{4}\$]{.math.inline} For numbers 26 -- 30, refer to the function [\$y = - 2\\sin{\\left( \\frac{x}{2} - \\frac{\\pi}{6} \\right) + 5}\$]{.math.inline} 26. What is the amplitude of the function? A. [ − 2]{.math.inline} B. {.math.inline} C. [\$\\frac{1}{2}\$]{.math.inline} D. [ − 5]{.math.inline} 27. What is the period of the graph of the function? A. [*π*]{.math.inline} B. [2*π*]{.math.inline} C. [3*π*]{.math.inline} D. [4*π*]{.math.inline} 28. What is the minimum value of the function? A. {.math.inline} B. {.math.inline} C. {.math.inline} D. {.math.inline} 29. What is the maximum value of the function? A. {.math.inline} B. {.math.inline} C. {.math.inline} D. {.math.inline} 30. What is the value of [*y*]{.math.inline} when [\$x = \\frac{2\\pi}{3}\$]{.math.inline}? A. {.math.inline} B. {.math.inline} C. {.math.inline} D. {.math.inline} 31. What is the equation of the sine function whose graph is the graph of [*y* = sin *x*]{.math.inline} shifted upward 2 units and shifted to the left by [\$\\frac{\\pi}{3}\$]{.math.inline} units? A. [\$y = \\sin{2(x + \\frac{\\pi}{3})}\$]{.math.inline} B. [\$y = \\sin{\\left( x + \\frac{\\pi}{3} \\right) + 2}\$]{.math.inline} C. [\$y = \\sin{\\left( x - \\frac{\\pi}{3} \\right) + 2}\$]{.math.inline} D. [\$y = \\sin{\\left( x - \\frac{\\pi}{3} \\right) - 2}\$]{.math.inline} 32. Which of the following is/are TRUE for [*x* = 60^∘^]{.math.inline}? I. [\$\\sin\\text{x\\ } = \\frac{\\sqrt{3}}{2}\$]{.math.inline} II. [\$\\tan\\text{x\\ } = \\sqrt{3}\$]{.math.inline} III.[sec x  = 2]{.math.inline} A. Only I B. Only II C. Only III D. all of the above 33. Which of the following is a value of [*x*]{.math.inline} for which [1 + sin *x* + cos^2^*x* = 0]{.math.inline}? A. [\$\\frac{2\\pi}{3}\$]{.math.inline} B. [\$\\frac{3\\pi}{2}\$]{.math.inline} C. [\$\\frac{\\pi}{4}\$]{.math.inline} D. [*π*]{.math.inline} 34. What is the equivalent value of [tan^2^*x* − sec^2^*x*]{.math.inline} for any real values of [*x*]{.math.inline}? A. {.math.inline} B. [2tan^2^*x* − 1]{.math.inline} C. [ − 1]{.math.inline} D. {.math.inline} 35. Which of the following statements is/are TRUE ? I. [\$\\cos{\\left( - \\frac{\\pi}{4} \\right)\\ } = \\cos{\\left( \\frac{\\pi}{4} \\right)\\ }\$]{.math.inline} II. [\$\\cos{\\left( - \\frac{11\\pi}{2} \\right)\\ } = 0\$]{.math.inline} III.[\$\\tan{\\left( - \\frac{3\\pi}{2} \\right)\\ } = undefined\$]{.math.inline} A. Only I B. Only II C. Only III D. all of the above 36. Which of the following characteristics is TRUE for [*y* = cos^ − 1^*x*]{.math.inline}? A. Range is the set of real numbers C. Domain is the set of real numbers B. Range is [ − 1]{.math.inline} and 1 inclusive D. the maximum value is 1 37. Which of the following is undefined? 38. What is the period of [*y* = 4tan 2*πx*]{.math.inline}? A. {.math.inline} B. [2*π*]{.math.inline} C. [\$\\frac{\\pi}{2}\$]{.math.inline} D. [\$\\frac{1}{2}\$]{.math.inline} Consider the function, [*y* = asin*b*(*x*−*c*) + *d*]{.math.inline} 39. What formula will give the period of the function? A. [\$\\frac{2\\pi}{b}\$]{.math.inline} B. [\$\\frac{2}{b}\$]{.math.inline} C. [2*π*(*b*)]{.math.inline} D. [*π*(*b*)]{.math.inline} 40. What parameter gives the value of the horizontal shift of the function? A. a B. b C. c D. d 41. If [*y* =  − 2cos (4*x*+*π*) − 9]{.math.inline}, which of the following is TRUE? A. amplitude of [ − 2]{.math.inline} units, period of [\$\\frac{\\pi}{2}\$]{.math.inline}, phase shift of [*π*]{.math.inline} units to the left, and vertical translation of 9 units downward B. amplitude of {.math.inline} units, period of [\$\\frac{\\pi}{2}\$]{.math.inline}, phase shift of [\$\\frac{\\pi}{4}\$]{.math.inline} units to the left, and vertical translation of 9 units downward C. amplitude of {.math.inline} units, period of [\$\\frac{\\pi}{2}\$]{.math.inline}, phase shift of [\$\\frac{\\pi}{4}\$]{.math.inline} units to the right, and vertical translation of 9 units upward D. amplitude of [ − 2]{.math.inline} units, period of [2*π*]{.math.inline}, phase shift of [\$\\frac{\\pi}{4}\$]{.math.inline} units to the right, and vertical translation of 9 units upward 42. Which of the following properties is/are NOT true for [\$f\\left( x \\right) = - 2\\sin{\\left( \\frac{\\pi}{3}x + \\frac{\\pi}{6} \\right) + 1}\$]{.math.inline}? A. amplitude of 2 B. maximum point of 2 C. period of 6 D. phase shift of [\$\\frac{1}{2}\$]{.math.inline} 43. What function/s whose domain is the set of all real numbers except [nπ]{.math.inline}, where n is any integer? A. Tangent and Secant C. Sine and Cosine B. Cotangent and Cosecant D. Tangent and Cotangent 44. What is the maximum value of [\$y = - 3\\sin{\\left( 9x - \\frac{2\\pi}{3} \\right) - 5}\$]{.math.inline}? A. [ − 2]{.math.inline} B. [ − 3]{.math.inline} C. {.math.inline} D. {.math.inline} 45. Which of the following is the graph of [*y* = cot *x*]{.math.inline}?  A. [84^∘^47^′^23.48″]{.math.inline} B. C. D.  For numbers 46-47. A per store clerk noticed that the population in the gerbil habitat varied sinusoidally with respect to time, in days. He carefully collected the data and graphed his resulting equation. 46. From the graph, what is the amplitude? A. 3 C. 17 B. 15 D. 32 47. What is the period? A. 25 C. 28 B. 27 D. 31 For numbers 48-50, refer to the graph of the sine function below. 48. What is the phase shift of the function? A. [\$\\frac{\\pi}{4}\$]{.math.inline} to the left C. [\$\\frac{\\pi}{4}\$]{.math.inline} to the right B. [\$\\frac{\\pi}{2}\$]{.math.inline} to the left D. [\$\\frac{\\pi}{2}\$]{.math.inline} to the right 49. For what values of [*x*]{.math.inline} is the function equal to zero? A. [\$\\frac{\\pi}{4},\\ \\frac{5\\pi}{4},\\ \\frac{9\\pi}{4},\\ \\frac{13\\pi}{4},\\ \\frac{17\\pi}{4}\$]{.math.inline} C. [\$\\frac{\\pi}{2},\\ \\frac{5\\pi}{2},\\ \\frac{9\\pi}{2},\\ \\frac{13\\pi}{2},\\ \\frac{17\\pi}{2}\$]{.math.inline} B. [\$\\frac{\\pi}{4},\\ \\frac{3\\pi}{4},\\ \\frac{5\\pi}{4},\\ \\frac{7\\pi}{4},\\ \\frac{9\\pi}{4}\$]{.math.inline} D. [\$\\frac{\\pi}{2},\\ \\frac{3\\pi}{2},\\ \\frac{5\\pi}{2},\\ \\frac{7\\pi}{2},\\ \\frac{9\\pi}{2}\$]{.math.inline} 50. What is the equation of the graph given above? A. [\$y = 3\\sin\\left( x + \\frac{\\pi}{4} \\right)\$]{.math.inline} C. [\$y = - 3\\sin\\left( x + \\frac{\\pi}{4} \\right)\$]{.math.inline} B. [\$y = 3\\sin\\left( x - \\frac{\\pi}{4} \\right)\$]{.math.inline} D. [\$y = - 3\\sin\\left( x - \\frac{\\pi}{4} \\right)\$]{.math.inline}