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Lesson: Solving Equations Using Inverse Trigonometric Functions

In this lesson, we will learn how to solve equations by using inverse trigonometric functions.

Sample Question Videos

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04:55

Worksheet • 15 Questions • 2 Videos

Q1:

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

Q2:

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

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

Q3:

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

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

Q4:

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

Q5:

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

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

Q6:

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

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

Q7:

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

Q8:

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

Q9:

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

  • A π‘š ∠ 𝐴 = 5 1 . 7 ∘
  • B π‘š ∠ 𝐴 = 0 . 9 ∘
  • C π‘š ∠ 𝐴 = 3 8 . 3 ∘
  • D π‘š ∠ 𝐴 = 0 . 7 ∘
  • E π‘š ∠ 𝐴 = 3 1 . 8 ∘

Q10:

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 .

Q11:

Find the measure of ∠ 𝐴 given 1 7 𝐴 βˆ’ 1 6 = 0 s i n where 𝐴 ∈  0 , πœ‹ 2  . Give the answer to the nearest second.

  • A 7 0 1 5 β€² ∘
  • B 1 0 9 4 5 β€² ∘
  • C 1 6 0 1 5 β€² ∘
  • D 1 9 4 5 β€² ∘

Q12:

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 [ ∘ ∘ .

Q13:

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

Q14:

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

Q15:

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