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Mu Alpha Theta National Convention: Hawaii, 2005 Trigonometry Topic Test – Alpha Division 1. Evaluate: tan 24 A) 2 3 B) 6 3 2 2 C) 2 3 6 2 2 3 D) 4 2( 3 1) 4 2( 3 1) E) NOTA 2. If sec( ) 2 , which of the following could equal? 3 7 A) B) C) D) 4 3 6 4 3. Simplify: sin 6 (x) 3sin 2 (x)cos2 (x) cos6 (x) A) 0 4. 5. E) NOTA B) 1 3 C) sin( x) cos(x) D) 1 sin 2 (2x) 4 Which of the following equations has cos(20) as a root? A) y 81x 4 144 x 2 64 B) y 8x 3 6x 1 C) y 10x 3 9x 2 30x 27 D) No such equation exists E) NOTA E) NOTA , ) is a point in space represented by cylindrical coordinates, what is the Cartesian 3 6 representation of the point? If (4, A) (1, 3 , 2 3 ) B) (2 3 , 2, ) C) (2, 2 3 , ) D) ( 3 , 3, 2) 3 6 E) NOTA 6. If f (x) 3sin( 4x) 5 , A is the amplitude of f (x) , B is the period of f (x) , C is the D B A? maximum value of f (x) , and D is the minimum value of f (x) , what is C A) 7. 29 4 B) C) 7 2 11 4 2 D) 13 4 2 E) NOTA Which of the following angle measures is coterminal to 3650? A) 130 B) 230 C) 40 Page 1 of 5 D) 50 E) NOTA Mu Alpha Theta National Convention: Hawaii, 2005 Trigonometry Topic Test – Alpha Division 8. Which of the following expressions is equal to sin( 33) sin(11) ? A) 4 sin 4 (11) 3sin 2 (11) C) sin( 44) 9. B) sin 2 (22) sin 2 (11) 3 2 D) sin (33) 2sin (22) sin(11) E) NOTA Evaluate tan(i ln 2) where i 1 and the domain of the tangent function has been expanded to include complexnumbers. A) 3i 5 B) 5i 3 C) i 2cos(i ln 2) D) No solution 10. What is the maximum of the real function f (x) 4sin x 3cos x ? 4 A) 4 B) 7 C) 5 D) arctan 3 11. Given sin(A)= A) E) NOTA E) NOTA 5 15 , cos(B)= , what is tan(A+B)? 13 17 21 220 B) 19 20 C) 171 140 D) 91 110 E) NOTA 12. If f (x) sin x , g(x) cos x , and h(x) f (x) g(x) . Find h( 8) . 2 A) 2 1 B) 2 C) 2 D) 2 4 E) NOTA 13. Which of the following describes the behavior of the graph y sin x at x 2? (where integer function)? x is the greatest A) continuous B) removable discontinuity C) jump discontinuity D) infinite discontinuity E) NOTA 3 14. What is the phase shift of y sin 3x ? 8 A) 3 8 B) 8 C) D) 8 Page 2 of 5 3 8 E) NOTA Mu Alpha Theta National Convention: Hawaii, 2005 Trigonometry Topic Test – Alpha Division 15. In ABC, BC 4 , mBAC 60 , and mABC 75 . What is the length of AB ? A) 2 6 B) 4 6 3 C) 6 22 6 3 D) 4 2 16. What is the name of the polar graph of r sin( ) cos( ) ? A) lemniscate B) cissoid C) limacon D) conic E) NOTA E) NOTA 17. What is the value of cos( ) if is the acute angle between the vectors <3,4> and <2,6>? 10 3 A) 10 B) 25 C) 1 2 D) 3 10 10 E) NOTA 18. Evaluate: cos(0) sin(0) cos sin cos sin cos sin 3 6 6 3 2 2 B) 2 2 3 A) 0 D) 3 3 C) 1 E) NOTA 19. If sin( x) cos( x) tan( x) cos(x) sec( x) 0 , what is the sum of all possible values for x on the interval 0,2 ? A) 3 B) 5 C) 9 2 D) 0 E) NOTA 20. How many of the following are equivalent to cos(2x) ? cot 2 (x) 1 ix ix e e 1 sin 2 (2x) cos4 (x) sin 4 (x) 2 cot 2 (x) 1 A) 1 B) 2 C) 3 D) 4 E) NOTA 21. In the figure below A and B lie on the circumference of circle C, if AB AC BC 1, what is the area of the shaded region (the region between the chord AB and the arc AB)? A) 3 3 2 B) 3 C) 6 3 4 D) Page 3 of 5 12 3 8 E) NOTA Mu Alpha Theta National Convention: Hawaii, 2005 Trigonometry Topic Test – Alpha Division 22. Evaluate sin( x) in the figure to the right. A) .8 B) .75 C) .6 D) Not enough information 23. Find the measure of the acute angle between the x-axis and the line r 5 A) arctan 2 2 B) arctan 5 C) arctan 10 arcsin( 2) D) arccos(5) E) NOTA 1 . 2sin 5cos E) NOTA 24. Two particles are at the same location at t = 0s and then begin to move away from each other at an angle of 60. If one particle is moving at 4 m/s and the other at 3 m/s, what is the square of the number of meters between them at t = 2s? A) 10 B) 13 C) 52 D) 100 E) NOTA D) 4 E) NOTA 25. What is the area of the graph enclosed by r sin ? A) 4 B) 2 C) 26. A right triangle has a hypotenuse of 4 and an angle with a sine of 1 3 . What is the length of the longer leg of the triangle? A) 4 3 B) 32 9 C) 8 2 3 D) 12 E) NOTA 27. Which of the following is equivalent to cis(12 ) cis(4)? A) cis(3) B) cis(8) C) cis(16) Page 4 of 5 D) cis(48) E) NOTA Mu Alpha Theta National Convention: Hawaii, 2005 Trigonometry Topic Test – Alpha Division 28. Which of the following is true for all values of x for which both the left and right sides of the equation are defined? sec(x) sin( x) tan( x) tan( x) I. csc(x) cos(x) cot( x) sin( 3x) cos(3x) 4 cos(2x) II. sin( x) cos(x) cos(4 x) 2cos(x) (sin( x) 2sin 3 (x)) III. cot(4 x) A) I only B) II only C) III only D) I, II, and III E) NOTA 29. A rhombus has an area of 24 square units and one of its diagonals, d, has a length of 8 units. If x is an angle not intersected by d, which of the following is equal to sin(x)? A) 7 25 B) 4 5 C) 24 25 D) 8 5 E) NOTA 30. Order the following numbers from least to greatest: cos(90), tan(/3), cot(315), sin(3/4) A) cot(315), cos(90), tan(/3), sin(3/4) B) tan(/3), sin(3/4), cos(90), cot(315) C) sin(3/4), cos(90), cot(315), tan(/3) D) cot(315), sin(3/4), cos(90), tan(/3) E) NOTA Page 5 of 5