Worksheet: Exact Values of Trigonometric Ratios

In this worksheet, we will practice finding exact circular function values.

Q1:

Find 𝜃 given s i n 𝜃 = 1 2 and c o s 𝜃 = 3 2 .

  • A 1 1 𝜋 6
  • B 𝜋 5
  • C 5 𝜋 6
  • D 𝜋 6
  • E0

Q2:

What is the value of t a n 𝜃 in the given triangle?

  • A 5 1 3
  • B 1 2 1 3
  • C 1 2 5
  • D 5 1 2
  • E 1 3 1 2

Q3:

Find the value of t a n t a n 2 2 4 5 6 0 .

  • A 3 2
  • B2
  • C 3 2
  • D 2

Q4:

Find the exact value of s i n 3 0 .

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

Q5:

Find t a n 𝐵 , given 𝐴 𝐵 𝐶 is a right-angled triangle at 𝐶 where 𝐴 𝐶 = 8 c m and 𝐵 𝐶 = 1 5 c m .

  • A 8 1 7
  • B 1 5 8
  • C 1 7 8
  • D 8 1 5

Q6:

Find the value of c o s 𝜋 3 .

  • A1
  • B 1 2
  • C 1
  • D 1 2

Q7:

Find the value of c o s 2 𝜋 3 .

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

Q8:

Find the value of s i n 3 𝜋 4 .

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

Q9:

Find the value of t a n 5 𝜋 6 .

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

Q10:

Find the value of c o s 5 𝜋 4 .

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

Q11:

Find t a n 𝐴 , given 𝐴 𝐵 𝐶 is a right-angled triangle at 𝐶 where 𝐴 𝐵 = 2 0 c m and 𝐵 𝐶 = 1 6 c m .

  • A 4 5
  • B 3 4
  • C 5 4
  • D 4 3

Q12:

Find the value of s e c 𝜋 4 .

  • A 2 3 3
  • B 2
  • C 2 3 3
  • D 2

Q13:

Find the value of s i n 𝜋 6 .

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

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