Worksheet: Solving Equations Using Inverse Trigonometric Functions

Download

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 𝑚∠𝐸 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 0≤𝑥<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 0≤𝜃<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 𝑚∠𝐴 to the nearest tenth of a degree.

Q6:

Find 𝑚∠𝐸 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=−1√3, where 0≤𝑥<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 2𝜃−√2=0cos and tan𝜃−1=0.

Q10:

Find the value of 𝑚∠𝐸 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 0≤𝑥<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 17𝐴−16=0sin where 𝐴∈0,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.

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