Lesson Worksheet: Solving Equations Using Inverse Trigonometric Functions Mathematics

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, 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∘

Q3:

Given that 𝐴 is an acute angle and that sin𝐴=0.8193, determine 𝑚∠𝐴 to the nearest tenth of a degree.

Q4:

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′′∘

Q5:

Find the smallest positive angle that satisfies both 2𝜃−√2=0cos and tan𝜃−1=0.

Q6:

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′′∘

Q7:

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

Q8:

Find the measure of ∠𝐴 given 17𝐴−16=0sin where 𝐴∈0,𝜋2. Give the answer to the nearest second.

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

Q9:

Find the measure of ∠𝑋 in degrees given √2𝑋=45sintan∘ where 𝑋 is an acute angle.

Q10:

Solve sin𝑥+𝜋=3𝜋2.

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

Q11:

Solve sin(𝑥)=𝜋4.

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

Q12:

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

Q13:

Find the value of sintancos2𝑋34𝑋3+2𝑋3 without using a calculator, given tan𝑋=1 where 𝑋 is an acute angle.

  • A12
  • B2
  • C√3
  • D√33
  • E1

Q14:

Find the value of cos2𝑋 without using a calculator, given 𝑋 where tan𝑋=1 is an acute angle.

  • A12
  • B1
  • C2
  • D0

Q15:

Find the value of 32𝑥2𝑥costan without using a calculator, given sintansin𝑥=3060∘∘where 𝑥 is an acute angle.

  • A2√39
  • B√32
  • C3√32
  • D2√33
  • E3

Q16:

Given that 𝑥 is an acute angle and 4(𝑥)=2√3cos, determine the value of 𝑥 in radians.

  • A𝜋4
  • B𝜋6
  • C𝜋16
  • D𝜋3
  • E𝜋12

Q17:

If the angle 𝜃 is in the standard position, cos𝜃=−√22, and sin𝜃=−√22, is it possible for 𝜃 to measure 135∘?

  • AYes
  • BNo

Q18:

Fill in the blank: Given that 𝑥 is an acute angle, if sin𝑥=𝑎 and −1<𝑎<1, then 𝑥=.

  • Acos𝑎
  • Bsin𝑥
  • Csin𝑎
  • D−𝑥sin
  • Ecos𝑥

Q19:

Find the value of 𝑥 that satisfies the equation tan∘𝑥=20. Round your answer to two decimal places.

Q20:

Find the value of 𝑥 that satisfies the equation cos∘𝑥=10.

Round your answer to two decimal places.

Q21:

Given that 𝑥 is an acute angle, find the value of 𝑥 that satisfies the equation sintan(2𝑥−1)=30∘. Round your answer to two decimal places.

Q22:

True or False: The acute angle 𝑥∘ that satisfies tan(𝑥+2)=2 is 61.43∘.

  • AFalse
  • BTrue

Q23:

True or False: The smallest positive angle 𝑥∘ that satisfies cos(𝑥+1)=0.1 is 84.26∘.

  • ATrue
  • BFalse

Q24:

Find the acute angle 𝑥∘ that satisfies sin(𝑥+2)=0.2. Round your answer to two decimal places.

Q25:

If 8𝜃−5=0tan, find 𝜃 to the nearest second.

  • A5759′41′′∘
  • B−320′19′′∘
  • C3210′29′′∘
  • D320′19′′∘
  • E8536′5′′∘

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