Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Lesson: Solving Trigonometric Equations with the Double-Angle Identity

Worksheet • 8 Questions

Q1:

Find all the possible solutions, that is, the general solution, of the equation s i n c o s s i n πœƒ πœƒ = √ 2 2 πœƒ .

  • A 𝑛 πœ‹ , Β± πœ‹ 4 + 2 𝑛 πœ‹ (where 𝑛 ∈ β„€ )
  • B Β± πœ‹ 4 + 2 𝑛 πœ‹ (where 𝑛 ∈ β„€ )
  • C 𝑛 πœ‹ , πœ‹ 4 + 2 𝑛 πœ‹ (where 𝑛 ∈ β„€ )
  • D 𝑛 πœ‹ , Β± πœ‹ 2 + 2 𝑛 πœ‹ (where 𝑛 ∈ β„€ )
  • E 𝑛 πœ‹ , βˆ’ πœ‹ 2 + 2 𝑛 πœ‹ (where 𝑛 ∈ β„€ )

Q2:

Find the general solution to the equation c o s s i n 3 π‘₯ = π‘₯ 4 .

  • A π‘₯ = 2 πœ‹ 1 3 + 8 𝑛 πœ‹ 1 3 , π‘₯ = βˆ’ 2 πœ‹ 1 1 + 8 𝑛 πœ‹ 1 1 , where 𝑛 ∈ β„€
  • B π‘₯ = πœ‹ 1 2 + 𝑛 πœ‹ 3 , π‘₯ = 2 πœ‹ 1 3 + 8 𝑛 πœ‹ 1 3 , where 𝑛 ∈ β„€
  • C π‘₯ = 2 πœ‹ 1 3 + 2 𝑛 πœ‹ 1 3 , π‘₯ = βˆ’ 2 πœ‹ 1 1 + 2 𝑛 πœ‹ 1 1 , where 𝑛 ∈ β„€
  • D π‘₯ = πœ‹ 1 2 + 𝑛 πœ‹ 3 , π‘₯ = βˆ’ 2 πœ‹ 1 1 + 8 𝑛 πœ‹ 1 1 , where 𝑛 ∈ β„€
  • E π‘₯ = 2 πœ‹ 1 3 + 4 𝑛 πœ‹ 1 3 , π‘₯ = βˆ’ 2 πœ‹ 1 1 + 4 𝑛 πœ‹ 1 1 , where 𝑛 ∈ β„€

Q3:

If 0 ≀ πœƒ < 1 8 0 ∘ ∘ , find the solution set of √ 2 πœƒ πœƒ βˆ’ πœƒ = 0 s i n c o s s i n .

  • A { 0 , 4 5 } ∘ ∘
  • B { 0 , 1 3 5 } ∘ ∘
  • C { 4 5 , 9 0 } ∘ ∘
  • D { 4 5 , 1 3 5 } ∘ ∘

Q4:

If 0 ≀ πœƒ < 1 8 0 ∘ ∘ , find the solution set of 2 πœƒ πœƒ + πœƒ = 0 s i n c o s s i n .

  • A { 0 , 1 2 0 } ∘ ∘
  • B { 9 0 , 1 2 0 } ∘ ∘
  • C { 0 , 3 0 } ∘ ∘
  • D { 0 , 6 0 } ∘ ∘

Q5:

Find the solution set for π‘₯ given c o s c o s 2 π‘₯ + 1 3 √ 3 π‘₯ = βˆ’ 1 9 where π‘₯ ∈ ] 0 , 2 πœ‹ [ .

  • A { 1 5 0 , 2 1 0 } ∘ ∘
  • B { 1 2 0 , 2 4 0 } ∘ ∘
  • C { 3 0 , 3 3 0 } ∘ ∘
  • D { 1 5 0 , 3 3 0 } ∘ ∘

Q6:

Find the solution set for π‘₯ given c o s c o s 2 π‘₯ + 5 √ 3 π‘₯ = βˆ’ 7 where π‘₯ ∈ ] 0 , 2 πœ‹ [ .

  • A { 3 0 , 3 3 0 } ∘ ∘
  • B { 1 5 0 , 2 1 0 } ∘ ∘
  • C { 3 0 , 3 0 0 } ∘ ∘
  • D { 6 0 , 2 4 0 } ∘ ∘

Q7:

Find πœƒ in degrees given s i n c o s πœƒ = 4 πœƒ where πœƒ is a positive acute angle.

Q8:

Find the set of possible solutions of 2 πœƒ πœƒ = 0 s i n c o s given πœƒ ∈ [ 0 , 3 6 0 [ ∘ ∘ .

  • A { 0 , 9 0 , 1 8 0 , 2 7 0 } ∘ ∘ ∘ ∘
  • B { 3 0 , 1 5 0 , 1 8 0 , 2 7 0 } ∘ ∘ ∘ ∘
  • C { 0 , 9 0 , 1 2 0 , 2 4 0 } ∘ ∘ ∘ ∘
  • D { 6 0 , 1 2 0 , 1 8 0 , 2 7 0 } ∘ ∘ ∘ ∘
Preview