Worksheet: Evaluating Trigonometric Functions with Special Angles

In this worksheet, we will practice evaluating the trigonometric functions with special angles and how to use them to evaluate trigonometric expressions.

Q1:

Find the value of costancsccos135+135+225+225.

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

Q2:

Calculate sincoscossin31545120330.

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

Q3:

Calculate 4330240270240+270135sinsincossecsincos.

  • A1
  • B 1
  • C 2
  • D2

Q4:

Find the value of 5(180𝜃)2430240+48330sinsintansin given that 5𝜃=4cos where 0<𝜃<180.

Q5:

Find the value of tan4𝜋3.

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

Q6:

Find the value of tan𝜋3.

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

Q7:

Find the value of sin7𝜋6.

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

Q8:

Find tan30.

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

Q9:

Evaluate sincoscoscot150(240)+2,130240.

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

Q10:

Find the value of tan7𝜋4.

  • A1
  • B 2
  • C 2
  • D 1
  • E 3

Q11:

Evaluate sincossincos960(210)+150240.

  • A 1 2
  • B 1 2
  • C1
  • D 1

Q12:

Find the value of sin𝜋6.

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

Q13:

The intensity of an electric current is given by 𝐶=152(75𝑡)cos 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 ) c o s c o s s i n 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 ) s i n c o s c o s 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

Q14:

Find the value of cos𝜋4.

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

Q15:

Find the value of sin5𝜋3.

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

Q16:

Find sin(690) without using a calculator.

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

Q17:

The intensity of an electric current is given by 𝐶=32(345𝑡)cos, 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 8
  • D 3 6 + 2

Q18:

Find the value of sin3𝜋4.

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

Q19:

Find the value of cos11𝜋6.

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

Q20:

Find the value of cos2𝜋3.

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

Q21:

Calculate sincoscossin315135240150.

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

Q22:

Find the value of sintancos2𝑋34𝑋3+2𝑋3 without using a calculator, given tan𝑋=1 where 𝑋 is an acute angle.

  • A 1 2
  • B2
  • C 3
  • D 3 3
  • E1

Q23:

Find the value of cos2𝑋 without using a calculator, given 𝑋 where tan𝑋=1 is an acute angle.

  • A 1 2
  • B1
  • C2
  • D0

Q24:

Find the value of 32𝑥2𝑥costan without using a calculator, given sintansin𝑥=3060where 𝑥 is an acute angle.

  • A 2 3 9
  • B 3 2
  • C 3 3 2
  • D 2 3 3
  • E3

Q25:

Find the value of cot15730 given csccotcot2𝑋+2𝑋=𝑋.

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

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