Worksheet: Evaluating Trigonometric Functions with Special Angles

In this worksheet, we will practice using function values of special angles to evaluate trigonometric expressions.

Q1:

Find the value of c o s t a n c s c c o s 1 3 5 + 1 3 5 + 2 2 5 + 2 2 5 .

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

Q2:

Calculate s i n c o s c o s s i n 3 1 5 4 5 1 2 0 3 3 0 .

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

Q3:

Calculate 4 3 3 0 2 4 0 2 7 0 2 4 0 + 2 7 0 1 3 5 s i n s i n c o s s e c s i n c o s 2 2 .

  • A2
  • B 1
  • C1
  • D 2

Q4:

Find the value of 5 ( 1 8 0 𝜃 ) 2 4 3 0 2 4 0 + 4 8 3 3 0 s i n s i n t a n s i n 2 2 given 5 𝜃 = 4 c o s where 0 < 𝜃 < 1 8 0 .

Q5:

Evaluate c o s c o s s i n s i n 5 5 4 5 7 9 1 5 5 5 4 5 7 9 1 5 .

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

Q6:

Find the value of t a n 4 𝜋 3 .

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

Q7:

Find the value of t a n 𝜋 3 .

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

Q8:

Find the value of s i n 7 𝜋 6 .

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

Q9:

Find t a n 3 0 .

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

Q10:

Evaluate s i n c o s c o s c o t 1 5 0 ( 2 4 0 ) + 2 1 3 0 2 4 0 .

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

Q11:

Find the value of t a n 7 𝜋 4 .

  • A 2
  • B1
  • C 2
  • D 1
  • E 3

Q12:

Evaluate s i n c o s s i n c o s 9 6 0 ( 2 1 0 ) + 1 5 0 2 4 0 .

  • A1
  • B 1
  • C 1 2
  • D 1 2

Q13:

Find the value of s i n 𝜋 6 .

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

Q14:

The intensity of an electric current is given by 𝐶 = 1 5 2 ( 7 5 𝑡 ) c o s where 𝑡 is the time in seconds. Rewrite the intensity after one second using sum and product formulae in terms of special angles.

  • A 1 5 2 ( 1 2 0 4 5 + 1 2 0 4 5 ) s i n c o s c o s s i n
  • B 1 5 2 ( 1 2 0 4 5 1 2 0 4 5 ) s i n c o s c o s s i n
  • C 1 5 2 ( 1 2 0 4 5 1 2 0 4 5 ) c o s c o s s i n s i n
  • D 1 5 2 ( 1 2 0 4 5 + 1 2 0 4 5 ) c o s c o s s i n s i n

Q15:

Find the value of c o s 𝜋 4 .

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

Q16:

Find the value of s i n 5 𝜋 3 .

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

Q17:

Find c s c ( 6 9 0 ) without using a calculator.

  • A 3
  • B 3
  • C 2
  • D2

Q18:

Evaluate s i n s i n c o s c o s 8 1 5 4 8 1 5 4 without using a calculator.

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

Q19:

The intensity of an electric current is given by 𝐶 = 3 2 ( 3 4 5 𝑡 ) c o s where 𝑡 is the time in seconds. Find the intensity after one second using sum and product formulae.

  • A 3 6 2
  • B 3 6 + 2 8
  • C 3 6 + 2
  • D 3 6 + 2 8

Q20:

Find the value of s i n 3 𝜋 4 .

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

Q21:

Find the value of c o s 1 1 𝜋 6 .

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

Q22:

Evaluate c o s c o s s i n s i n ( 𝑥 + 1 7 8 ) ( 𝑥 9 2 ) + ( 𝑥 + 1 7 8 ) ( 𝑥 9 2 ) .

  • A 1 2
  • B1
  • C 1
  • D0

Q23:

Find the value of c o s 2 𝜋 3 .

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

Q24:

Evaluate c o s c o s s i n s i n ( 𝑥 + 2 3 5 ) ( 3 5 𝑥 ) ( 𝑥 + 2 3 5 ) ( 3 5 𝑥 ) without using a calculator.

  • A 1 2
  • B1
  • C 1
  • D0

Q25:

Calculate s i n c o s c o s s i n 3 1 5 1 3 5 2 4 0 1 5 0 .

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

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