Worksheet: Solving Equations Using Cofunction Identities

In this worksheet, we will practice solving trigonometric equations using cofunction identities.

Q1:

Find the value of sec(90+𝜃) given csc𝜃=178 where 0<𝜃<90.

  • A 1 7 8
  • B 8 1 7
  • C 8 1 7
  • D 1 7 8

Q2:

Find the value of cot(270+𝜃) given tan𝜃=43 where 90<𝜃<180.

  • A 4 3
  • B 3 4
  • C 4 3
  • D 3 4

Q3:

Find the value of cos(180+𝜃) given sin(90𝜃)=717 where 𝜃 is the smallest positive angle.

  • A 4 1 5 1 7
  • B 7 1 7
  • C 4 1 5 1 7
  • D 7 1 7

Q4:

Find the general solution of the equation sin(90𝜃)=12.

  • A ± 𝜋 6 + 2 𝜋 𝑛 where 𝑛
  • B ± 2 𝜋 3 + 2 𝜋 𝑛 where 𝑛
  • C ± 𝜋 3 + 2 𝜋 𝑛 where 𝑛
  • D ± 5 𝜋 6 + 2 𝜋 𝑛 where 𝑛

Q5:

Find the value of sintantan(180𝜃)+(90𝜃)(270𝜃) given cos𝜃=45 where 90<𝜃<180.

  • A 3 5
  • B 4 9 1 5
  • C 4 9 1 5
  • D 3 5

Q6:

Find the value of sin(90𝜃) given sin𝜃=35 where 180𝜃<270.

  • A 4 5
  • B 3 5
  • C 3 5
  • D 4 5

Q7:

Find the value of sin(270𝜃) given sin𝜃=1213 where 90<𝜃<180.

  • A 5 1 3
  • B 5 1 3
  • C 1 2 1 3
  • D 1 2 1 3

Q8:

Find the value of cot𝜋22𝐵 given tan𝐵=32 where 3𝜋2<𝐵<2𝜋.

  • A 5 6
  • B 6 5
  • C 1 2 5
  • D 5 6

Q9:

Find sin8𝜃 given sec(90+𝜃)2=0 where 180<𝜃<270.

  • A 1 2
  • B 3
  • C 1 2
  • D 3 2

Q10:

Find the value of cot(𝜃90) given sec𝜃=1715 where 90<𝜃<180.

  • A 8 1 5
  • B 1 5 8
  • C 8 1 5
  • D 1 5 8

Q11:

Find the value of coscos(360𝐵)(90𝐵) given tan𝐵=43 where 0<𝐵<𝜋2.

  • A 1 5
  • B 1 5
  • C0
  • D 6 5
  • E 6 5

Q12:

Find sin6𝜃 given cossin2𝜃=7𝜃 where 𝜃 is a positive acute angle.

  • A 1 2
  • B1
  • C 3 2
  • D 2 2

Q13:

Find cot(903𝜃) given tancot𝜃=5𝜃 where 𝜃 is a positive acute angle.

  • A1
  • B 3
  • C 2 2
  • D 3 3

Q14:

Find the value of 𝜃 that satisfies sincos4𝜃𝜋3=4𝜃 where 𝜃0,𝜋2.

  • A 5 𝜋 2 4
  • B 𝜋 4 8
  • C 𝜋 2 4
  • D 5 𝜋 4 8

Q15:

Find the value of 𝜃 that satisfies tancot𝜃+952=𝜃+352 where 0𝜃<90.

Q16:

Which of the following is the general solution of the equation cscsec6𝜃=3𝜃?

  • A 𝜋 1 8 2 𝜋 𝑛 9 or 𝜋6+2𝜋𝑛3, where 𝑛
  • B 𝜋 1 8 + 2 𝜋 𝑛 9 or 𝜋6+2𝜋𝑛3, where 𝑛
  • C 𝜋 9 + 𝜋 𝑛 9 or 𝜋3𝜋𝑛3, where 𝑛
  • D 2 𝜋 9 + 2 𝜋 𝑛 9 or 2𝜋3+2𝜋𝑛3, where 𝑛

Q17:

Find the set of values satisfying sincostan1575+3(90+𝜃)=0, where 0𝜃<360.

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

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