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.

  • A178
  • B817
  • C817
  • D178

Q2:

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

  • A43
  • B34
  • C43
  • D34

Q3:

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

  • A41517
  • B717
  • C41517
  • D717

Q4:

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

  • A±𝜋6+2𝜋𝑛 where 𝑛
  • B±2𝜋3+2𝜋𝑛 where 𝑛
  • C±𝜋3+2𝜋𝑛 where 𝑛
  • D±5𝜋6+2𝜋𝑛 where 𝑛

Q5:

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

  • A35
  • B4915
  • C4915
  • D35

Q6:

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

  • A45
  • B35
  • C35
  • D45

Q7:

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

  • A513
  • B513
  • C1213
  • D1213

Q8:

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

  • A56
  • B65
  • C125
  • D56

Q9:

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

  • A12
  • B3
  • C12
  • D32

Q10:

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

  • A815
  • B158
  • C815
  • D158

Q11:

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

  • A15
  • B15
  • C0
  • D65
  • E65

Q12:

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

  • A12
  • B1
  • C32
  • D22

Q13:

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

  • A1
  • B3
  • C22
  • D33

Q14:

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

  • A5𝜋24
  • B𝜋48
  • C𝜋24
  • D5𝜋48

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?

  • A𝜋182𝜋𝑛9 or 𝜋6+2𝜋𝑛3, where 𝑛
  • B𝜋18+2𝜋𝑛9 or 𝜋6+2𝜋𝑛3, where 𝑛
  • C𝜋9+𝜋𝑛9 or 𝜋3𝜋𝑛3, where 𝑛
  • D2𝜋9+2𝜋𝑛9 or 2𝜋3+2𝜋𝑛3, where 𝑛

Q17:

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

  • A{60, 240}
  • B{30, 210}
  • C{120, 300}
  • D{60, 120}

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