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.

  • A1+2
  • B21
  • C1+22
  • D221

Q2:

Calculate sincoscossin31545120330.

  • A34
  • B14
  • C14
  • D34

Q3:

Calculate 4330240270240+270135sinsincossecsincos.

  • A1
  • B1
  • C2
  • D2

Q4:

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

Q5:

Find the value of tan4𝜋3.

  • A3
  • B33
  • C2
  • D2
  • E3

Q6:

Find the value of tan𝜋3.

  • A3
  • B22
  • C3
  • D22
  • E12

Q7:

Find the value of sin7𝜋6.

  • A12
  • B12
  • C3
  • D22
  • E22

Q8:

Find tan30.

  • A13
  • B12
  • C32
  • D13

Q9:

Evaluate sincoscoscot150(240)+2,130240.

  • A14
  • B14
  • C34
  • D34

Q10:

Find the value of tan7𝜋4.

Q11:

Evaluate sincossincos960(210)+150240.

  • A12
  • B12
  • C1
  • D1

Q12:

Find the value of sin𝜋6.

  • A32
  • B32
  • C12
  • D12
  • E2

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.

  • A152(12045+12045)coscossinsin
  • B152(12045+12045)sincoscossin
  • C152(1204512045)sincoscossin
  • D152(1204512045)coscossinsin

Q14:

Find the value of cos𝜋4.

  • A32
  • B32
  • C12
  • D22
  • E22

Q15:

Find the value of sin5𝜋3.

  • A32
  • B22
  • C23
  • D32
  • E22

Q16:

Find sin(690) without using a calculator.

  • A13
  • B12
  • C13
  • D12

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.

  • A362
  • B36+28
  • C36+28
  • D36+2

Q18:

Find the value of sin3𝜋4.

  • A33
  • B22
  • C2
  • D33
  • E22

Q19:

Find the value of cos11𝜋6.

  • A22
  • B32
  • C32
  • D12
  • E12

Q20:

Find the value of cos2𝜋3.

  • A3
  • B22
  • C2
  • D12
  • E12

Q21:

Calculate sincoscossin315135240150.

  • A34
  • B14
  • C14
  • D34

Q22:

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

  • A12
  • B2
  • C3
  • D33
  • E1

Q23:

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

  • A12
  • B1
  • C2
  • D0

Q24:

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

  • A239
  • B32
  • C332
  • D233
  • E3

Q25:

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

  • A12
  • B2+3
  • C1+2
  • D23

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