Worksheet: Simplifying Trigonometric Expressions in Terms of Sine and Cosine

In this worksheet, we will practice simplifying and rewriting expressions of trigonometric functions using sine and cosine functions only.

Q1:

Simplify s i n c o s t a n c o t 𝜃 𝜃 ( 𝜃 + 𝜃 ) .

Q2:

Expand s i n 𝜃 + 𝜋 6 using sum and difference formulas.

  • A 1 2 ( 𝜃 + 𝜃 ) s i n c o s
  • B 1 2 𝜃 + 3 𝜃 s i n c o s
  • C 2 𝜃 + 3 𝜃 s i n c o s
  • D 1 2 3 𝜃 + 𝜃 s i n c o s

Q3:

Simplify c o s c o s s e c ( 1 8 0 𝜃 ) ( 9 0 𝜃 ) ( 𝜃 1 8 0 ) .

  • A 𝜃 c o s 2
  • B1
  • C c o s 𝜃
  • D s i n 𝜃

Q4:

Simplify s i n ( 𝜃 9 0 ) .

  • A c o s 𝜃
  • B s i n 𝜃
  • C 𝜃 s i n
  • D 𝜃 c o s

Q5:

Simplify t a n c s c s i n 𝜃 𝜃 ( 9 0 𝜃 ) .

Q6:

Find the value of 1 1 2 8 s e c 2 .

  • A s i n 2 8
  • B c o s 2 8
  • C c o s 2 2 8
  • D s i n 2 2 8

Q7:

Simplify 5 𝑎 𝑎 c o s t a n 2 .

  • A 5 2 2 𝑎 c o s
  • B s i n 2 𝑎
  • C c o s 2 𝑎
  • D 5 2 2 𝑎 s i n

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