Worksheet: Solving Equations Using Inverse Trigonometric Functions

In this worksheet, we will practice solving equations by using inverse trigonometric functions in the first quadrant.

Q1:

If 𝐸 is an acute angle, find 𝑚𝐸 given sin𝐸=0.791. Give the answer to the nearest second.

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

Q2:

Find the set of values satisfying sin𝑥=22, where 0𝑥<2𝜋.

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

Q3:

Find the value of 𝜃 given 2𝜃+1=0cos where 𝜃 is the largest angle in the range 0𝜃<360.

Q4:

Find, to the nearest tenth of a degree, the measure of the angle of cos𝐴=0.6194.

Q5:

Given that sin𝐴=0.8193, determine 𝑚𝐴 to the nearest tenth of a degree.

Q6:

Find 𝑚𝐸 given tan𝐸=18.5845 and 𝐸 is an acute angle. Give the answer to the nearest second.

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

Q7:

Find the set of values satisfying tan𝑥=13, where 0𝑥<2𝜋.

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

Q8:

Find the set of values satisfying tan𝜃=0 given 0<𝜃<360.

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

Q9:

Find the smallest positive angle that satisfies both 2𝜃2=0cos and tan𝜃1=0.

Q10:

Find the value of 𝑚𝐸 given that 𝐸 is an acute angle and cos𝐸=0.5201. Give the answer to the nearest second.

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

Q11:

Find the angle 𝐴 to the nearest tenth of a degree, knowing that tan𝐴=0.86 and 𝐴(0,180).

Q12:

Find the set of values satisfying cos𝑥=12, where 0𝑥<2𝜋.

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

Q13:

Find the measure of 𝑋 in degrees given 2𝑋=60costan where 𝑋 is an acute angle.

Q14:

Find the measure of 𝐴 given 17𝐴16=0sin where 𝐴0,𝜋2. Give the answer to the nearest second.

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

Q15:

Find the measure of 𝑋 in degrees given tantan𝑋=345 where 𝑋 is an acute angle.

Q16:

Solve sin𝑥+𝜋=3𝜋2.

  • A 𝑥 = 1
  • B 𝑥 = 0
  • C 𝑥 = 2 2
  • D 𝑥 = 1 2
  • E 𝑥 = 1

Q17:

Solve sin(𝑥)=𝜋4.

  • A 𝜃 = 1 2
  • B 𝜃 = 3 2
  • C 𝜃 = 𝜋 4
  • D 𝜃 = 2 2

Q18:

Find the value of 𝑋 given tan𝑋4=3 where 𝑋4 is an acute angle.

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