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 𝑚𝐸 given sin𝐸=0.791. Give the answer to the nearest second.

  • A374315
  • B382038
  • C521645

Q2:

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

  • A𝑚𝐴=51.7
  • B𝑚𝐴=31.8
  • C𝑚𝐴=0.7
  • D𝑚𝐴=38.3
  • E𝑚𝐴=0.9

Q3:

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

Q4:

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

  • A894130
  • B865512
  • C614258

Q5:

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

Q6:

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

  • A583940
  • B272844
  • C312020

Q7:

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

Q8:

Find the measure of 𝐴 given 17𝐴16=0sin where 𝐴0,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
  • C3
  • D33
  • 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=3060where 𝑥 is an acute angle.

  • A239
  • B32
  • C332
  • D233
  • E3

Q16:

Given that 𝑥 is an acute angle and 4(𝑥)=23cos, 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
  • D𝑥sin
  • Ecos𝑥

Q19:

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

Q20:

Find the value of 𝑥 that satisfies the equation cos𝑥=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(2𝑥1)=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 8𝜃5=0tan, find 𝜃 to the nearest second.

  • A575941
  • B32019
  • C321029
  • D32019
  • E85365

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