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1) If csc Θ = , find sin Θ. A) B) C) D) 2) If sin Θ = 1/4, find sin(-Θ) A) B) C) D) 3) f sin Θ = and cos Θ = , find tan Θ. A) 3 B) ½ C) 1 D) 2 4) If csc Θ = A) , what is cot Θ? B) C) D) 5) If tan Θ = 1/2, what is sec Θ? A) B) C) D) 6) If sec ( A) )= , what is csc Θ? B) C) D) 7) Simplify the expression: sec^2(x)*cot(x) A) sin(x)cos(x) B) cos(x) C) tan(x) D) sec(x)csc(x) 8) Simplify the expression: A) tan^2x B) sec^2x C) csc^2x D) sin^2x 9) Which is a factor of: csc^2x - 11cscx + 10 A) csc(x) + 2 B) csc(x) - 2 C) csc(x) + 1 D) csc(x) – 1 10) Simplify A) sin(x) B) cos(x) C) sec(x) D) csc(x) 11) When verifying a trigonometric identity, which of the following guidelines should you follow? A) If you do not know what to do, do not try anything. It is better to not do anything than it is to mess up. B) Work on simplifying the less complicated side of the identity first. C) Look for opportunities to use the fundamental identities. D) Try to make the identity more complicated. 12) When verifying a trigonometric identity, which of the following guidelines should not be followed? A) Work on simplifying the more complicated side of the identity first. B) Set the identity equal to zero to solve for the variable. C) Always try something. Even making an attempt that leads to a dead end provides insight. D) Look for opportunities to factor an expression, add fractions, square a binomial, or create a monomial denominator. 13) Which of the following identities would be the best option to use to verify the identity below? 14) What would be the best next step for verifying the identity? 15) Which of the following would be the best first step for verifying the identity below? 16) What would be the best next step for verifying the identity below? 17) What would be the best next step for verifying the identity below? 18) What would be the best first step for verifying the identity below? 19) The following expression was simplified incorrectly. In which line was an error first made when simplifying the identity shown below? A. Line 1 B. Line 2 C. Line 3 D. Line 4 20) The identity below was verified incorrectly. In which line was an error first made? A. Line 1 B. Line 2 C. Line 3 Line 4 21) Evaluate the expression. cos(x)sin(90° - x) + sin2(x) A. 0 B. 1 C. 2x D. 2sin(x) 22)Evaluate the expression. tan2(x) + sec2(x) A. 0 B. 1 C. -1 D. None of the above. Complete the sentence given below. The factors of sec2(x) - sin2(x) are _______________. A. sec(x) - sin(x) B. sec(x) + sin(x) C. (sec(x) - sin(x))(sec(x) + sin(x)) D. (sec(x) - sin(x))(sec(x) - sin(x)) 24) What is a factor of: 2sec2(x) - 3sec(x) - 2 A. 2sec(x) + 3 B. 2sec(x) + 1 C. sec(x) - 2 D. Both B and C 25) What is a factor of: tan2x + 2tan(x)cos(x) + cos2(x) A. tan(x) + cos(x) B. tan(x) - cos(x) C. 2tan(x) - cos(x) D. Both A and B 26) Solve the equation for 0 ≤ x < 360. tan2x - tan(x) = 2 A. 135 degrees B. 315 degrees C. no solution D. Both A and B 27) Solve the equation for 0 ≤ x < 360. A. 45 degrees B. 63 degrees C. Both A and B D. Does not exist. Solve the equation for 0 ≤ x < 360. tan(x) + 6 = 3tan(x) + 4 A. 45 and 225 degrees B. 135 and 315 degrees C. 135 and 225 degrees D. 225 and 315 degrees 29) Solve the equation for 0 ≤ x < 360. sin(x) + A. 45 and 225 degrees B. 135 and 315 degrees C. 135 and 225 degrees D. 225 and 315 degrees 30) Solve the equation for 0 ≤ x < 360. 3csc(x) + 5 = csc(x) + 9 A. 30 and 150 degrees B. 150 and 330 degrees C. 60 and 120 degrees D. 120 and 300 degrees 31) Given Sin(A) = ⅗ and Cos(B) = 8/17 in Quadrant I, find Sin(A+B). A) 24/80 B) 84/85 C) 60/80 D) 60/85 32) Given Sin(A) = ⅗ and Cos(B) = 8/17 in Quadrant I, find Cos(A+B). A) 32/80 B) -45/85 C) -13/80 D) -13/85 33) Given Sin(A) = ⅗ and Cos(B) = 8/17 in Quadrant I, find Tan(A+B). A) 0.8 B) -1.72 C) -4.21 D) -6.46 34) Given Sin(A) = ⅗ and Cos(B) = 8/17 in Quadrant I, what is the Quadrant of A+B ? A) I B) II C) III D) IV 35) Given Tan(A) = 5 in Quadrant III and Sin(B) = ⅔ in Quadrant II, find Sin(A-B). 36) Given Tan(A) = 5 in Quadrant III and Sin(B) = ⅔ in Quadrant II, what is the Quadrant of A-B? A) I B) II C) III D) IV 37) 38) 39) 40) 41) 42) 43) Given tan(A) = 2 and A is in Quadrant I, find sin(2A). A) 0 B) 1 C) 1/2 D) 4/5 44) Given tan(A) = 2 and A is in Quadrant I, find cos(2A). A) 0 B) 1 C) 1/2 D) -3/5 45) Given tan(A) = 2 and A is in Quadrant I, find tan(2A). A) -1/3 B) 2/3 C) -4/3 D) -2/3 46) Find sin(A)cos(B) A) ½ (sin(105) + sin(345)) B) ½ (sin(105) - sin(345)) C) ½ (sin(345) + cos(105)) D) ½ (sin(345) - cos(105)) 47) If angle A is 45 degrees and angle B is 60 degrees. Find cos(A)sin(B) A) ½ (sin(105) + sin(345)) B) ½ (sin(105) - sin(345)) C) ½ (sin(345) + cos(105)) D) ½ (sin(345) - cos(105)) 48) If angle A is 45 degrees and angle B is 60 degrees. Find sin(A)sin(B) A) ½ (cos(345) + cos(105)) B) ½ (cos(105) - cos(345)) C) ½ (cos(345) - cos(105)) D) ½ (cos(105) + cos(345)) 49) If angle A is 45 degrees and angle B is 60 degrees. Find cos(A)cos(B) A) ½ (cos(345) + cos(105)) B) ½ (cos(105) - cos(345)) C) ½ (cos(345) - cos(105)) D) ½ (cos(105) + cos(345)) 50. if angle A is 45 degrees and angle B is 60 degrees. Find cos(A)cos(B)½ (cos(345) + cos(105)) ½ (cos(105) - cos(345)) ½ (cos(345) - cos(105)) ½ (cos(105) + cos(345))
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Explanation & Answer

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1) If csc Θ =

, find sin Θ.

A)

B)

C)

D)

2) If sin Θ = 1/4, find sin(-Θ)
A)
B)
C)
D)

3) f sin Θ =

and cos Θ =

, find tan Θ.

A) 3
B) ½
C) 1
D) 2
4) If csc Θ =
A)

, what is cot Θ?

B)
C)
D)

5) If tan Θ = 1/2, what is sec Θ?
A)

B)

C)

D)

6) If sec (
A)

)=

, what is csc Θ?

B)

C)

D)

7) Simplify the expression: sec^2(x)*cot(x)
A) sin(x)cos(x)
B) cos(x)

C) tan(x)
D) sec(x)csc(x)

8) Simplify the expression:

A) tan^2x
B) sec^2x
C) csc^2x
D) sin^2x

9) Which is a factor of: csc^2x - 11cscx + 10
A) csc(x) + 2
B) csc(x) - 2
C) csc(x) + 1
D) csc(x) – 1

10) Simplify

A) sin(x)
B) cos(x)
C) sec(x)
D) csc(x)

11) When verifying a trigonometric identity, which of the following guidelines
should you follow?
A) If you do not know what to do, do not try anything. It is better to not do
anything than it is to mess up.
B) Work on simplifying the less complicated side of the identity first.
C) Look for opportunities to use the fundamental identities.
D) Try to make the identity more complicated.

12) When verifying a trigonometric identity, which of the following guidelines
should not be followed?
A)

Work on simplifying the more complicated side of the identity first.

B) Set the identity equal to zero to solve for the variable.
C) Always try something. Even making an attempt that leads to a dead
end provides insight.
D) Look for opportunities to factor an expression, add fractions, square a
binomial, or create a monomial denominator.

13) Which of the following identities would be the best option to use to verify the
identity below?

14) What would be the best next step for verifying the identity?

15) Which of the following would be the best first step for verifying the identity
below?

16) What would be the best next step for verifying the identity below?

17) What would be the best next step for verifying the identity below?

18) What would be the best first step for verifying the identity below?

19) The following expression was simplified incorrectly. In which line was an
error first made when simplifying the identity shown below?

A. Line ...


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