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

Worksheet: Solving Equations by Using Inverse Trigonometric Functions

Q1:

Find, to the nearest tenth of a degree, the measure of the angle of c o s 𝐴 = 0 . 6 1 9 4 .

Q2:

Find the value of π‘š ∠ 𝐸 given that ∠ 𝐸 is an acute angle and c o s 𝐸 = 0 . 7 7 9 . Give the answer to the nearest second.

  • A 3 7 5 5 β€² 7 β€² β€² ∘
  • B 5 1 1 0 β€² 9 β€² β€² ∘
  • C 3 8 4 9 β€² 5 1 β€² β€² ∘

Q3:

Find the value of π‘š ∠ 𝐸 given that ∠ 𝐸 is an acute angle and c o s 𝐸 = 0 . 5 2 0 1 . Give the answer to the nearest second.

  • A 2 7 2 8 β€² 4 4 β€² β€² ∘
  • B 3 1 2 0 β€² 2 0 β€² β€² ∘
  • C 5 8 3 9 β€² 4 0 β€² β€² ∘

Q4:

If 𝐸 is an acute angle. Find the value of π‘š ∠ 𝐸 given s i n 𝐸 = 0 . 7 9 1 . Give the answer to the nearest second.

  • A 3 8 2 0 β€² 3 8 β€² β€² ∘
  • B 3 7 4 3 β€² 1 5 β€² β€² ∘
  • C 5 2 1 6 β€² 4 5 β€² β€² ∘

Q5:

Given that s i n 𝐴 = 0 . 8 1 9 3 , determine π‘š ∠ 𝐴 to the nearest tenth of a degree.

Q6:

Find π‘š ∠ 𝐸 given t a n 𝐸 = 1 8 . 5 8 4 5 and ∠ 𝐸 is an acute angle. Give the answer to the nearest second.

  • A 6 1 4 2 β€² 5 8 β€² β€² ∘
  • B 8 9 4 1 β€² 3 0 β€² β€² ∘
  • C 8 6 5 5 β€² 1 2 β€² β€² ∘

Q7:

Find the angle 𝐴 to the nearest tenth of a degree, knowing that t a n 𝐴 = 0 . 8 6 and 𝐴 ∈ ( 0 , 1 8 0 ) ∘ ∘ .

Q8:

Find the set of values satisfying c o s π‘₯ = 1 2 , where 0 ≀ π‘₯ < 2 πœ‹ .

  • A  πœ‹ 3 , 4 πœ‹ 3 
  • B  πœ‹ 3 
  • C { 0 , 2 πœ‹ }
  • D  πœ‹ 3 , 5 πœ‹ 3 
  • E  πœ‹ 3 , 2 πœ‹ 

Q9:

Find the set of values satisfying s i n π‘₯ = βˆ’ √ 2 2 , where 0 ≀ π‘₯ < 2 πœ‹ .

  • A  5 πœ‹ 4 , 9 πœ‹ 4 
  • B  5 πœ‹ 4 
  • C { 0 , 2 πœ‹ }
  • D  5 πœ‹ 4 , 7 πœ‹ 4 
  • E  3 πœ‹ 4 , 7 πœ‹ 4 

Q10:

Find the set of values satisfying t a n π‘₯ = βˆ’ 1 √ 3 , where 0 ≀ π‘₯ < 2 πœ‹ .

  • A  7 πœ‹ 6 , 5 πœ‹ 6 
  • B  πœ‹ 6 , 7 πœ‹ 6 
  • C { 0 , 2 πœ‹ }
  • D  5 πœ‹ 6 , 1 1 πœ‹ 6 
  • E  5 πœ‹ 6 , 2 πœ‹ 

Q11:

Find the set of values satisfying t a n πœƒ = 0 given 0 < πœƒ < 3 6 0 ∘ ∘ .

  • A { 1 8 0 } ∘
  • B { 0 } ∘
  • C { 1 2 0 , 9 0 } ∘ ∘
  • D { 0 , 1 8 0 } ∘ ∘

Q12:

Find the size of in degrees given where is an acute angle.

  • A
  • B
  • C
  • D

Q13:

Find the size of in degrees given where is an acute angle.

  • A
  • B
  • C
  • D

Q14:

Find the smallest positive angle that satisfies both 2 πœƒ βˆ’ √ 2 = 0 c o s and t a n πœƒ βˆ’ 1 = 0 .

Q15:

Find the measure of given where . Give the answer to the nearest second.

  • A
  • B
  • C
  • D