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Worksheet: Solving Trigonometric Equations

Q1:

Suppose is a point on a unit circle corresponding to the angle of . Is there another point on the unit circle that represents an angle in the interval and has the same -coordinate as ? If yes, give the angle.

  • Ayes,
  • Byes,
  • Cyes,
  • Dno
  • Eyes,

Q2:

Consider , a point on a unit circle corresponding to the angle of . Is there another point on the unit circle representing an angle in the interval that has the same -coordinate as ? If yes, give the angle.

  • Ayes,
  • Byes,
  • Cno
  • Dyes,
  • Eyes,

Q3:

Consider , a point on a unit circle corresponding to the angle of . Is there another point on the unit circle that has the same -coordinate as and represents an angle in the interval ? If yes, give the angle.

  • Ayes,
  • Byes,
  • Cno
  • Dyes,
  • Eyes,

Q4:

Consider that is a point on a unit circle corresponding to the angle of . Is there another point on the unit circle that has the same -coordinate as and represents an angle in the interval ? If yes, give the angle.

  • Ayes,
  • Byes,
  • Cyes,
  • Dyes,
  • Eno

Q5:

Suppose is a point on a unit circle corresponding to the angle of . Is there another point on the unit circle representing an angle in the interval that has the same tangent value? If yes, give the angle.

  • Ayes,
  • Byes,
  • Cyes,
  • Dyes,
  • Eno

Q6:

Is there a value of the tangent function that is obtained from ONLY one angle in the interval ? If yes, give the angle.

  • Ayes,
  • Byes,
  • Cno
  • Dyes, 0
  • Eyes,

Q7:

What is the general solution of ?

  • A or where
  • B or where
  • C or where
  • D or where

Q8:

Find all the possible general solutions of .

  • A :
  • B :
  • C :
  • D :
  • E :

Q9:

What is the general solution of ?

  • A or where is an integer.
  • B or where is an integer.
  • C or where is an integer.
  • D or where is an integer.

Q10:

Find all the possible general solutions of .

  • A :
  • B :
  • C :
  • D :
  • E :

Q11:

What is the general solution of ?

  • A or where is an integer.
  • B or where is an integer.
  • C or where is an integer.
  • D or where is an integer.

Q12:

What is the general solution of ?

  • A or where
  • B or where
  • C or where
  • D or where

Q13:

Find all the possible general solutions of .

  • A :
  • B :
  • C :
  • D :
  • E :

Q14:

What is the general solution of ?

  • A or where
  • B or where
  • C or where
  • D or where

Q15:

Find the set of values satisfying given .

  • A
  • B
  • C
  • D

Q16:

Find the smallest positive angle that satisfies both and .

Q17:

Find the value of given where is the largest angle in the range .

Q18:

Find in degrees given where is the smallest positive angle.

Q19:

Find the set of values satisfying where .

  • A
  • B
  • C
  • D
  • E

Q20:

Find the value of given where is an acute angle. Give the answer to the nearest minute.

  • A
  • B
  • C
  • D

Q21:

Find the value of given where is an acute angle. Give the answer to the nearest minute.

  • A
  • B
  • C
  • D

Q22:

Find the value of given where is an acute angle. Give the answer to the nearest minute.

  • A
  • B
  • C
  • D

Q23:

Find the value of given where is an acute angle.

Q24:

Find the set of values satisfying where .

  • A
  • B
  • C
  • D

Q25:

Find the set of values satisfying where .

  • A
  • B
  • C
  • D

Q26:

Find all the possible general solutions of .

  • A.
  • B.
  • C.
  • D.
  • E.

Q27:

Find all the possible general solutions of .

  • A,