Exam 3 Math 1022 LSU

If -1<b<0, then which of the following statements best describes the solution to the equation cosθ=b on the interval of [0,2π)?

There are EXACTLY TWO SOLUTIONS to the equation cosθ-b on the interval [0,2π). ****θ=π- cos⁻¹(-b)***** ****θ=π+cos⁻¹(-b)*****

Which of the following is not a variation of a Pythagorean Identity? a. 1-cos²θ=csc²θ b. -cos²θ=sin²θ-1 c. tan²θ=sec²θ-1 d. sin²θ=1-cos²θ

a. 1-cos²θ=csc²θ

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. A trigonometric identity is valid for all values of the independent variable ****for which both sides of the identity are defined.****

Which of the following is the correct sum formula for the cosine function? a. cos (α+β)= cos α cos β - sin a sin β b. cos (α+β)= sin α cos β - cos a sin β c. cos (α+β)= cos α cos β + sin a sin β d. cos (α+β)= sin α cos β + cos a sin β

a. cos (α+β)= cosαcosβ-sinαsinβ

Which of the following is NOT a valid double-angle formula for cosine? ********************a. cos2θ= 2sin²θ - 1 b. cos2θ= 1 - 2sin²θ c. cos2θ= cos²θ - sin²θ d. cos2θ= 2 cos²θ - 1

a. cos2θ= 2sin²θ - 1

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. If more than one term appears in the denominator of an expression, try using long division to simplify the expression.

Which of the following is NOT a valid strategy for solving the given equation? a. To solved the equation cos²θ= sinθcosθ, first subtract sinθcosθ from both sides, then factor out the common factor of cosθ on the left side. b. To solve the equation cos²θ=sinθcosθ, ***FIRST DIVIDE**** both sides by cosθ. c. To solve sin2θ+2cosθsin2θ=0, first factor out the common factor of sin2θ on the left side. d. To solve the equation sinθ+cosθ=1, first square both sides of the equation.

b. To solve the equation cos^2θ=sinθcosθ, FIRST DIVIDE both sides by cosθ.

Which of the following can best be evaluated using the sum formula for the sine function? a. cos (2sin⁻¹(-1/√2)) ************************b. sin (tan⁻¹+cos⁻¹ (√3/2)) c. sin (1/2 cos⁻¹ (-1/2)) d. sin (cos⁻¹ (-1/2))

b. sin (tan⁻¹+cos⁻¹ (√3/2))

Which of the following is the correct sum formula for the tangent function? a. tan (α+β)= (tan α - tan β)/1+tan α tan β b. tan (α+β)= (tan α + tan β)/1- tan α tan β c. tan (α+β)= (tan α - tan β)/1- tan α tan β d. tan (α+β)= (tan α + tan β)/1+ tan α tan β

b. tan (α+β)= (tanα+tanβ)/1-tanαtan β

Using the technique of changing to sines and cosines to verify an identity, determine which of the following is not an identity. a. (secθ cscθ)/cotθ= sec²θ b. cotθ sin²θ=sinθcosθ ********************************c. (sinθcscθ)/cos²θ=tan²θ d. sin² t= tan t cot t - cos²t

c. (sinθcscθ)/cos²θ=tan²θ

If α/2 is an angle with a terminal side lying in Quad III, then which of the following expressions is equivalent to sin (α/2)? a. √(1+cos α)/2 b. √(1-cos α)/2 ******************c. -√(1- cos α)/2 d. -√(1+ cos α)/2

c. -√(1- cos α)/2

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 [0,2π) *********c. IT IS POSSIBLE for a trigonometric equation to have general solutions but not have a solution on the interval [0,2π).************* d. Every trigonometric equation has at least one solution on the interval [0,2π)

c. IT IS POSSIBLE for a trigonometric equation to have general solutions but not have a solution on the interval [0,2π).

Which of the following is the correct difference formula for the sine function? a. sin (α-β)= cos α cos β - sin α sin β b. sin (α-β)= cos α cos β + sin α sin β c. sin (α-β)= sin α cos β - cos α sin β d. sin (α-β)= sin α cos β + cos α sin β

c. sin (α-β)= sin α cos β - cos α sin β

Which of the following is NOT a trigonometric equation that is linear in form? a. tan (θ+π/6) + 1 = 0 b. sin θ/2 = -√3/2 ********c. sinθcosθ = -1/2******** d. √3 tanθ + 1 = 0

c. sinθcosθ = -1/2

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. tan (α-β)= (tanα-tanβ)/1+tanαtanβ

If α/2 is an angle with a terminal side lying in Quad IV, then which of the following expressions is NOT equivalent to tan (α/2)? a. (1 - cos α) / sin α b. -√(1- cos α) / (1+ cos α) *****c. √(1- cos α) / (1+ cos α)***** d. sin α/1 + cos α

c. √(1- cos α) / (1+ cos α)

If α/2 is an angle with a terminal side lying in Quad IV, then which of the following expressions is NOT equivalent to tan (α/2)? a. (1 - cos α) / sin α b. -√(1- cos α) / (1+ cos α) *****c. √(1- cos α) / (1+ cos α)****** d. sin α/1 + cos α

c. √(1- cos α) / (1+ cos α)

Which of the following is not a valid property of trigonometric functions? a. sec (-θ)= sec θ b. csc (-θ)= - csc θ c. tan (-θ)= - tan θ ****d. cot (-θ)= cot θ****

d. cot(-θ)=cotθ