Worksheet: Evaluating Trigonometric Expressions Using Half Angle Identities

In this worksheet, we will practice using a half-angle identity to find an exact value and simplify expressions.

Q1:

Using the half angle formulas, find the exact value of c o s 𝜋 8 .

  • A 2 + 2 4
  • B 2 2 2
  • C 2 2 4
  • D 2 + 2 2
  • E 2 2

Q2:

Using the half-angle formulas, find the exact value of c o s ( 1 5 ) .

  • A 3 4
  • B 3 + 2 4
  • C 3 2
  • D 3 + 2 2
  • E 3 2 2

Q3:

Using the half-angle formulas, find the exact value of s i n ( 1 5 ) .

  • A 2 3 4
  • B 2 + 3 2
  • C 2 + 3 4
  • D 2 3 2
  • E 1 2

Q4:

Using the half angle formulas, find the exact value of s i n 𝜋 8 .

  • A 2 2 4
  • B 2 + 2 2
  • C 2 + 2 4
  • D 2 2 2
  • E 2 2

Q5:

Find the value of 6 4 4 0 8 0 3 0 0 1 6 0 c o s c o s c o s c o s without using a calculator.

  • A 1 4
  • B4
  • C 1 4
  • D 4

Q6:

Evaluate 1 6 1 5 7 3 0 1 5 7 3 0 s i n c o s without using a calculator.

  • A 4 2
  • B 8 2
  • C 8
  • D 4 2

Q7:

Evaluate 8 1 0 5 1 0 5 s e c c s c without using a calculator.

  • A 2 3
  • B 4
  • C 4 3 3
  • D 2

Q8:

Evaluate 2 3 1 5 3 c o s 2 without using a calculator.

  • A 1 4
  • B 3 2
  • C 3 2
  • D 3 2

Q9:

Evaluate 1 2 1 5 c o s 2 without using a calculator.

  • A 1 4
  • B 3 2
  • C 3 4
  • D 3 4

Q10:

Find the value of s i n c o s s i n c o s 𝜋 1 6 𝜋 1 6 𝜋 1 6 𝜋 1 6 3 3 without using a calculator.

  • A 1 2
  • B 1 4 2
  • C 1 2
  • D 1 4 2

Q11:

Using the half angle formulas, find the exact value of t a n ( 1 5 ) .

  • A 1 3
  • B 2 + 3
  • C 1 3
  • D 2 3
  • E 1 + 3

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.