Exam 3 Math 1022 LSU
Which of the following is NOT a valid double-angle formula for cosine? a. cos2O= 2sin^2O - 1 b. cos2O= 1 - 2sin^2O c. cos2O= cos^2O - sin^2O d. cos2O= 2 cos^2O - 1
A
Which of the following is not a variation of a Pythagorean Identity? a. 1-cos^2O=csc^2O b. -cos^2O=sin^2O-1 c. tan^2O=sec^2O-1 d. sin^2O=1-cos^2O
A
Which of the following is the correct sum formula for the cosine function? a. cos (a+B)= cos a cos B - sin a sin B b. cos (a+B)= sin a cos B - cos a sin B c. cos (a+B)= cos a cos B + sin a sin B d. cos (a+B)= sin a cos B + cos a sin B
A
Which of the following is true? a. A trigonometric identity is valid for all values of the independent variable for which both sides of the identity are defined. b. Verifying a trigonometric identity is the process of bringing all terms to one side and solving for the variable c. There is only one correct way to verify a trigonometric identity. d. A trigonometric identity is valid for values of the independent variable that are angles belonging to one of the four special families of angles.
A
Which of the following can best be evaluated using the sum formula for the sine function? a. cos (2sin^-1(-1/sqrt2)) b. sin (tan^-1+cos^-1 (sqrt3/2)) c. sin (1/2 cos^-1 (-1/2)) d. sin (cos^-1 (-1/2))
B
Which of the following is NOT a valid strategy for solving the given equation? a. To solved the equation cos^2O= sinOcosO, first subtract sinOcosO from both sides, then factor out the common factor of cosO on the left side. b. To solve the equation cos^2O=sinOcosO, first divide both sides by cosO. c. To solve sin2O+2cosOsin2O=o, first factor out the common factor of sin2O on the left side. d. To solve the equation sinO+cosO=1, first square both sides of the equation.
B
Which of the following is not a process commonly used to verify an identity? a. If a single term appears in the denominator of a quotient, try separating the quotient into two or more quotients. b. If more than one term appears in the denominator of an expression, try using long division to simplify the expression. c. Use a known identity to make a substitution. d. If the denominator of a quotient contains an expression of the form A+B, try multiplying the numerator and denominator by the conjugate A-B.
B
Which of the following is the correct sum formula for the tangent function? a. tan (a+B)= (tan a - tan B)/1+tan a tan B b. tan (a+B)= (tan a + tan B)/1- tan a tan B c. tan (a+B)= (tan a - tan B)/1- tan a tan B d. tan (a+B)= (tan a + tan B)/1+ tan a tan B
B
If a/2 is an angle with a terminal side lying in Quad III, then which of the following expressions is equivalent to sin (a/2)? a. sqrt (1+cos a)/2 b. sqrt (1-cos a)/2 c. - sqrt (1- cos a)/2 d. - sqrt (1+ cos a)/2
C
If a/2 is an angle with a terminal side lying in Quad IV, then which of the following expressions is NOT equivalent to tan (a/2)? a. (1 - cos a)/ sin a b. - sqrt (1- cos a)/ (1+ cos a) c. sqrt (1- cos a)/ (1+ cos a) d. sin a/ 1 + cos a
C
Using the technique of changing to sines and cosines to verify an identity, determine which of the following is not an identity. a. (secO cscO)/cotO= sec^2O b. cotO sin^2O=sinOcosO c. (sinO cscO)/cos^2O=tan^2O d. sin^2 t= tan t cot t - cos^2t
C
Which of the following can best be evaluated using the half-angle formula for the sine function? a. sin (1/2 cos^-1(-2)) b. sin (tan^-1(1) + cos^-1(sqrt 3/2)) c. sin (1/2 cos^-1 (-2/3)) d. sin (cos^-1(-1/2))
C
Which of the following is NOT a trigonometric equation that is linear in form? a. tan (O+pi/6) + 1=0 b. sin O/2= -sqrt(3)/2 c. sinOcosO=-1/2 d. sqrt(3) tanO+1=0
C
Which of the following is the correct difference formula for the sine function? a. sin (a-B)= cos a cos B - sin a sin B b. sin (a-B)= cos a cos B + sin a sin B c. sin (a-B)= sin a cos B - cos a sin B d. sin (a-B)= sin a cos B + cos a sin B
C
Which of the following is the correct difference formula for the tangent function? a. tan (a-B)= (tan a + tan B)/1- tan a tan B b. tan (a-B)= (tan a + tan B)/ 1 + tan a tan B c. tan (a-B)= (tan a - tan B)/ 1 + tan a tan B d. tan (a-B)= (tan a - tan B)/ 1 - tan a tan B
C
Which of the following statements is true? a. It is not possible for a trigonometric equation to have infinitely many solutions. b. Every trigonometric equation has at least two distinct solutions on the interval [0,2pi) c. It is possible for a trigonometric equation to have general solutions but not have a solution on the interval [0,2pi). d. Every trigonometric equation has at least one solution on the interval [0,2pi)
C
Which of the following is not a valid property of trigonometric functions? a. sec (-O)= sec O b. csc (-O)= - csc O c. tan (-O)= - tan O d. cot (-O)= cot O
D
If -1<b<0, then which of the following statements best describes the solution to the equation cosO=b on the interval of [0,2pi)?
There are exactly two solutions to the equation cosO-b on the interval [0,2pi). One solution O = pi- cos^-1(-b), the other solution is O=pi+cos^-1(-b)
