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Lesson Worksheet: Solving Trigonometric Equations with the Double-Angle Identity Mathematics • 10th Grade

In this worksheet, we will practice solving trigonometric equations using the double-angle identity.

Q1:

Find the general solution to the equation cossin3π‘₯=π‘₯4.

  • Aπ‘₯=2πœ‹13+2π‘›πœ‹13, π‘₯=βˆ’2πœ‹11+2π‘›πœ‹11, where π‘›βˆˆβ„€
  • Bπ‘₯=πœ‹12+π‘›πœ‹3, π‘₯=βˆ’2πœ‹11+8π‘›πœ‹11, where π‘›βˆˆβ„€
  • Cπ‘₯=2πœ‹13+4π‘›πœ‹13, π‘₯=βˆ’2πœ‹11+4π‘›πœ‹11, where π‘›βˆˆβ„€
  • Dπ‘₯=πœ‹12+π‘›πœ‹3, π‘₯=2πœ‹13+8π‘›πœ‹13, where π‘›βˆˆβ„€
  • Eπ‘₯=2πœ‹13+8π‘›πœ‹13, π‘₯=βˆ’2πœ‹11+8π‘›πœ‹11, where π‘›βˆˆβ„€

Q2:

If πœƒβˆˆ(180,360)∘∘ and sincosπœƒ+πœƒ=βˆ’1, find the value of πœƒ.

Q3:

Find all the solutions of the equation sincosπ‘₯2π‘₯2=12 for 0≀π‘₯≀90∘. Write the answer approximated to the nearest whole angle in degrees.

  • Aπ‘₯=60∘
  • Bπ‘₯=45∘
  • Cπ‘₯=0∘
  • Dπ‘₯=30∘
  • Eπ‘₯=90∘

Q4:

Given that sincosπ‘₯+π‘₯=βˆ’713 and 0<π‘₯<2πœ‹, determine the possible values of cos2π‘₯.

  • A120169,βˆ’120169
  • B169119,βˆ’169119
  • C119169,βˆ’119169
  • D169120,βˆ’169120

Q5:

Find the set of possible solutions of 2πœƒπœƒ=0sincos given πœƒβˆˆ[0,360)∘∘.

  • A{30,150,180,270}∘∘∘∘
  • B{60,120,180,270}∘∘∘∘
  • C{0,90,180,270}∘∘∘∘
  • D{0,90,120,240}∘∘∘∘

Q6:

Find the solution set for π‘₯ given coscos2π‘₯+13√3π‘₯=βˆ’19 where π‘₯∈(0,2πœ‹).

  • A{150,210}∘∘
  • B{120,240}∘∘
  • C{150,330}∘∘
  • D{30,330}∘∘

Q7:

Solve tansinο€»π‘₯2=π‘₯, where 0≀π‘₯<2πœ‹.

  • Aπ‘₯∈0,πœ‹2
  • Bπ‘₯∈0,πœ‹2,3πœ‹2,2πœ‹οΈ
  • Cπ‘₯∈0,πœ‹4,πœ‹,3πœ‹4
  • Dπ‘₯∈0,πœ‹2,3πœ‹2
  • Eπ‘₯∈0,πœ‹4

Q8:

By using the half angle formula sincosο€»π‘₯2=ο„ž1βˆ’π‘₯2, or otherwise, solve the equation sincosο€»π‘₯2+π‘₯=1, where 0≀π‘₯<2πœ‹.

  • Aπ‘₯=0,13πœ‹,53πœ‹οΈ
  • Bπ‘₯=0,16πœ‹,56πœ‹οΈ
  • Cπ‘₯=0,13πœ‹,56πœ‹οΈ
  • Dπ‘₯=0,13πœ‹οΈ
  • Eπ‘₯=0,16πœ‹οΈ

Q9:

Find the set of solutions in the range 0<π‘₯<180 for the equation (π‘₯+π‘₯)=22π‘₯sincossin.

  • A{45,105,165}∘∘∘
  • B{45,75,105}∘∘∘
  • C{15,75,90}∘∘∘
  • D{90,210,330}∘∘∘
  • E{45,75,165}∘∘∘

Q10:

Find the set of possible values of π‘₯ which satisfy 1√π‘₯βˆ’π‘₯=2coscosοŠͺ where 0<π‘₯<360∘∘.

  • A{45,150,240,300}∘∘∘∘
  • B{45,135,225,315}∘∘∘∘
  • C{45,135}∘∘
  • D{45,135,210,330}∘∘∘∘

This lesson includes 20 additional questions and 160 additional question variations for subscribers.

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