Worksheet: Solving Reciprocal Trigonometric Equations

In this worksheet, we will practice solving trigonometric equations involving secant, cosecant, and cotangent over different intervals in degrees and radians.

Q1:

Find the value of 𝜃 that satisfies c s c 𝜃 2 = 0 where 𝜃 0 , 𝜋 2 .

Q2:

Find the set of values satisfying 3 𝜃 = 1 c o t given 0 < 𝜃 < 3 6 0 .

  • A { 3 0 0 , 2 4 0 }
  • B { 6 0 , 3 0 0 }
  • C { 1 2 0 , 3 0 0 }
  • D { 6 0 , 2 4 0 }

Q3:

Find 𝜃 in degrees given s e c ( 1 8 0 + 𝜃 ) = 2 3 3 where 𝜃 is the smallest positive angle.

Q4:

Find the set of values satisfying s i n c o t 𝜃 𝜃 = 1 2 where 0 𝜃 9 0 .

  • A { 1 8 0 , 1 3 5 }
  • B { 3 0 , 3 3 0 }
  • C { 3 0 , 1 8 0 }
  • D

Q5:

Find the value of 𝜃 that satisfies c o t 𝜃 3 3 = 0 where 𝜃 0 , 𝜋 2 .

Q6:

Find the value of 𝜃 that satisfies c s c 𝜃 2 = 0 where 𝜃 0 , 𝜋 2 .

Q7:

Find the value of 𝜃 that satisfies s e c 𝜃 2 = 0 where 𝜃 0 , 𝜋 2 .

Q8:

Find the set of values satisfying c o t 𝜃 = 1 given 0 < 𝜃 < 3 6 0 .

  • A { 1 3 5 , 2 2 5 }
  • B { 4 5 , 2 2 5 }
  • C { 2 2 5 , 3 1 5 }
  • D { 1 3 5 , 3 1 5 }

Q9:

Find the set of values satisfying s i n c o t 𝜃 𝜃 = 2 2 where 0 𝜃 < 3 6 0 .

  • A { 1 8 0 , 3 0 }
  • B
  • C { 1 2 0 , 9 0 }
  • D { 4 5 , 3 1 5 }

Q10:

Find 𝜃 in degrees given c o t ( 1 8 0 + 𝜃 ) = 1 where 𝜃 is the smallest positive angle.

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