# Worksheet: Solving Trigonometric Equations

Q1:

Find the value of which gives the maximum value of the equation where .

• A
• B
• C
• D

Q2:

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,
• Bno
• Cyes,
• Dyes,
• Eyes,

Q3:

Find all the possible general solutions of .

• A , , ,
• B , , ,
• C , , ,
• D , , ,
• E ,

Q4:

Find the value of which gives the minimum value of the equation where .

• A
• B
• C
• D

Q5:

Find the general solution to the equation .

• A , , where
• B , , where
• C , , where
• D , , where
• E , , where

Q6:

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

• A
• B
• C
• D

Q7:

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,
• Cyes,
• Dno
• Eyes,

Q8:

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

• Ayes, 0
• Byes,
• Cyes,
• Dno
• Eyes,

Q9:

Find the possible values of in the expression given where is the greatest angle in the range . Give the angle to the nearest minute.

• A or
• B or
• C or
• D or

Q10:

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

• A
• B
• C
• D

Q11:

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

• A
• B
• C
• D

Q12:

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

• A
• B
• C
• D

Q13:

Find the possible values of in the expression where , given where . Give the answer to the nearest second.

• A or
• B or
• C or
• D or

Q14:

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,
• Cyes,
• Dno
• Eyes,

Q15:

Find the solution set of given where .

• A
• B
• C
• D

Q16:

Find the value of that gives the minimum value of given where .

Q17:

Find the value of that gives the maximum value of given where .

Q18:

Find the set of values satisfying , where .

• A ,
• B ,
• C ,
• D ,

Q19:

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.

• Ano
• Byes,
• Cyes,
• Dyes,
• Eyes,

Q20:

Find the set of solutions for given , where .

• A
• B
• C
• D

Q21:

Find the set of values satisfying where .

• A
• B
• C
• D

Q22:

Find the set of solutions for given where .

• A
• B
• C
• D

Q23:

Find the set of values satisfying where . Give the answer to the nearest minute.

• A
• B
• C
• D

Q24:

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,
• Bno
• Cyes,
• Dyes,
• Eyes,

Q25:

Find the value of given , where and where , and . Give the answer to the nearest minute.

• A
• B
• C
• D