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Worksheet: Angle Sum and Difference Identities

Q1:

Simplify .

  • A
  • B
  • C0
  • D

Q2:

Simplify .

  • A
  • B
  • C0
  • D

Q3:

Simplify .

  • A
  • B
  • C0
  • D

Q4:

Given that , find the value of in degrees.

  • A
  • B
  • C
  • D
  • E

Q5:

Evaluate .

  • A
  • B
  • C
  • D

Q6:

Evaluate .

  • A
  • B
  • C
  • D

Q7:

Evaluate .

  • A
  • B
  • C
  • D

Q8:

Find .

  • A
  • B
  • C
  • D

Q9:

Find .

  • A
  • B
  • C
  • D

Q10:

Given that , where , and , where , find the exact value of .

  • A
  • B
  • C
  • D
  • E

Q11:

Given that , where , and , where , find the exact value of .

  • A
  • B
  • C
  • D
  • E

Q12:

Given that , where , and , where , find the exact value of .

  • A
  • B
  • C
  • D
  • E

Q13:

Given that , where , and , where , find the exact value of .

  • A
  • B
  • C
  • D
  • E

Q14:

Given that , where , and , where , find the exact value of .

  • A
  • B
  • C
  • D
  • E

Q15:

Given that , where , and , where , find the exact value of .

  • A
  • B
  • C
  • D
  • E

Q16:

Find given where and where .

  • A
  • B
  • C
  • D
  • E

Q17:

Find without using a calculator given and where and are acute angles.

  • A
  • B
  • C
  • D

Q18:

Find given and where and are acute angles.

  • A
  • B
  • C
  • D
  • E

Q19:

In triangle , and are acute angles, where and . Without using a calculator, find the value of .

  • A
  • B
  • C
  • D
  • E

Q20:

Using the relation , find an expression for in terms of and which holds when .

  • A
  • B
  • C
  • D
  • E

Q21:

Let us consider the two shown figures, each showing two points on the unit circle.

How is the figure on the right obtained from the figure on the left?

  • Aby rotating by an angle of about the origin
  • Bby rotating by an angle of about the origin
  • Cby rotating by an angle of about the origin
  • Dby rotating by an angle of about the origin
  • Eby rotating by an angle of about the origin

What can you say about the triangles and ?

  • AThey are different.
  • BThey are isosceles.
  • CThey are congruent.
  • DThey are equilateral.
  • EThey are similar.

Find the coordinates of , , , and .

  • A, , ,