Worksheet: Solving Equations Using Inverse Trigonometric Functions

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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.

  • A3743′15′′∘
  • B3820′38′′∘
  • C5216′45′′∘

Q2:

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

  • A5𝜋4,7𝜋4
  • B3𝜋4,7𝜋4
  • C5𝜋4,9𝜋4
  • D5𝜋4
  • E{0,2𝜋}

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.

  • A𝑚∠𝐴=51.7∘
  • B𝑚∠𝐴=31.8∘
  • C𝑚∠𝐴=0.7∘
  • D𝑚∠𝐴=38.3∘
  • E𝑚∠𝐴=0.9∘

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.

  • A8941′30′′∘
  • B8655′12′′∘
  • C6142′58′′∘

Q7:

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

  • A5𝜋6,11𝜋6
  • B7𝜋6,5𝜋6
  • C{0,2𝜋}
  • D𝜋6,7𝜋6
  • E5𝜋6,2𝜋

Q8:

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

  • A{0}∘
  • B{0,180}∘∘
  • C{180}∘
  • D{120,90}∘∘

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.

  • A5839′40′′∘
  • B2728′44′′∘
  • C3120′20′′∘

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.

  • A𝜋3,4𝜋3
  • B𝜋3
  • C𝜋3,2𝜋
  • D𝜋3,5𝜋3
  • E{0,2𝜋}

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.

  • A7015′∘
  • B16015′∘
  • C10945′∘
  • D1945′∘

Q15:

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

Q16:

Solve sin𝑥+𝜋=3𝜋2.

  • A𝑥=−1
  • B𝑥=0
  • C𝑥=√22
  • D𝑥=12
  • E𝑥=1

Q17:

Solve sin(𝑥)=𝜋4.

  • A𝜃=12
  • B𝜃=√32
  • C𝜃=𝜋4
  • D𝜃=√22

Q18:

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

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