Worksheet: Solving Equations Using Inverse Trigonometric Functions

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In this worksheet, we will practice solving equations by using inverse trigonometric functions.

Q1:

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

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

Q2:

Find the set of values satisfying s i n 𝑥 = − √ 2 2 , where 0 ≤ 𝑥 < 2 𝜋 .

  • A 5 𝜋 4 , 9 𝜋 4
  • B 5 𝜋 4
  • C { 0 , 2 𝜋 }
  • D 5 𝜋 4 , 7 𝜋 4
  • E 3 𝜋 4 , 7 𝜋 4

Q3:

Find the value of 𝜃 given 2 𝜃 + 1 = 0 c o s where 𝜃 is the largest angle in the range 0 ≤ 𝜃 < 3 6 0 ∘ ∘ .

Q4:

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

  • A 𝑚 ∠ 𝐴 = 3 1 . 8 ∘
  • B 𝑚 ∠ 𝐴 = 3 8 . 3 ∘
  • C 𝑚 ∠ 𝐴 = 0 . 7 ∘
  • D 𝑚 ∠ 𝐴 = 5 1 . 7 ∘
  • E 𝑚 ∠ 𝐴 = 0 . 9 ∘

Q5:

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

Q6:

Find 𝑚 ∠ 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 ′ 5 8 ′ ′ ∘
  • B 8 9 4 1 ′ 3 0 ′ ′ ∘
  • C 8 6 5 5 ′ 1 2 ′ ′ ∘

Q7:

Find the set of values satisfying t a n 𝑥 = − 1 √ 3 , where 0 ≤ 𝑥 < 2 𝜋 .

  • A 7 𝜋 6 , 5 𝜋 6
  • B 𝜋 6 , 7 𝜋 6
  • C { 0 , 2 𝜋 }
  • D 5 𝜋 6 , 1 1 𝜋 6
  • E 5 𝜋 6 , 2 𝜋

Q8:

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

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

Q9:

Find the smallest positive angle that satisfies both 2 𝜃 − √ 2 = 0 c o s and t a n 𝜃 − 1 = 0 .

Q10:

Find the value of 𝑚 ∠ 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 ′ 4 4 ′ ′ ∘
  • B 3 1 2 0 ′ 2 0 ′ ′ ∘
  • C 5 8 3 9 ′ 4 0 ′ ′ ∘

Q11:

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 [ ∘ ∘ .

Q12:

Find the set of values satisfying c o s 𝑥 = 1 2 , where 0 ≤ 𝑥 < 2 𝜋 .

  • A 𝜋 3 , 4 𝜋 3
  • B 𝜋 3
  • C { 0 , 2 𝜋 }
  • D 𝜋 3 , 5 𝜋 3
  • E 𝜋 3 , 2 𝜋

Q13:

Find the measure of ∠ 𝑋 in degrees given 2 𝑋 = 6 0 c o s t a n ∘ where 𝑋 is an acute angle.

Q14:

Find the measure of ∠ 𝐴 given 1 7 𝐴 − 1 6 = 0 s i n where 𝐴 ∈ 0 , 𝜋 2 . Give the answer to the nearest second.

  • A 1 9 4 5 ′ ∘
  • B 1 0 9 4 5 ′ ∘
  • C 1 6 0 1 5 ′ ∘
  • D 7 0 1 5 ′ ∘

Q15:

Find the measure of ∠ 𝑋 in degrees given t a n t a n 𝑋 = √ 3 4 5 ∘ where 𝑋 is an acute angle.

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