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Worksheet: Evaluating Trigonometric Functions with Special Angles

In this worksheet, we will practice finding the trigonometric function values for 30-, 45-, and 60-degree angles.

Q1:

Find the value of s i n c o s π‘₯ + 𝑦 given π‘₯ and 𝑦 are complementary angles in the ratio 2 1 : . Give the answer to four decimal places.

Q2:

Find the value of 𝑋 given 9 𝑋 = 6 0 6 0 3 0 c o s t a n t a n 2 ∘ 2 ∘ 2 ∘ .

  • A 3 1 6
  • B 1 7 2
  • C 1 4
  • D 1 3 6

Q3:

Find given and is an acute angle.

  • A
  • B
  • C
  • D

Q4:

Find the value of s i n t a n c o s ο€Ό 2 𝑋 3  ο€Ό 4 𝑋 3  + ο€Ό 2 𝑋 3  without using a calculator, given t a n 𝑋 = 1 where 𝑋 is an acute angle.

  • A2
  • B √ 3 3
  • C 1 2
  • D √ 3
  • E1

Q5:

Find the value of c o s 2 𝑋 without using a calculator, given 𝑋 where t a n 𝑋 = 1 is an acute angle.

  • A 1 2
  • B2
  • C1
  • D0

Q6:

Find the value of without using a calculator, given where is an acute angle.

  • A
  • B
  • C
  • D
  • E3

Q7:

Find the value of 1 + 6 0 3 0 3 0 t a n t a n c o s ∘ ∘ 2 ∘ .

  • A8
  • B4
  • C 3 8
  • D 8 3

Q8:

Find the value of 𝑋 in degrees given c o s ( 𝑋 + 1 9 ) = 1 √ 2 where 𝑋 + 1 9 is an acute angle.

Q9:

Find the value of c o s t a n s i n 2 ∘ 2 ∘ 2 ∘ 6 0 βˆ’ 2 4 5 βˆ’ 6 3 0 .

  • A βˆ’ 9 4
  • B βˆ’ 2 3 4
  • C βˆ’ 1 9 4
  • D βˆ’ 1 3 4

Q10:

Find the value of c o t 1 5 7 3 0 β€² ∘ given c s c c o t c o t 2 𝑋 + 2 𝑋 = 𝑋 .

  • A βˆ’ 2 βˆ’ √ 3
  • B 2 + √ 3
  • C 1 + √ 2
  • D βˆ’ 1 βˆ’ √ 2

Q11:

Find the value of t a n s i n c o s 2 ∘ 2 ∘ 2 ∘ 3 0 + 4 0 + 7 1 3 5 .

  • A 4 7 6
  • B βˆ’ 4 7 6
  • C βˆ’ 2 3 6
  • D 2 3 6

Q12:

Find the value of 2 4 5 3 0 c o s s i n ∘ ∘ .

  • A √ 2 4
  • B √ 6 3
  • C √ 6 2
  • D √ 2 2

Q13:

Find the value of c o s s i n s i n t a n t a n 6 0 3 0 βˆ’ 6 0 6 0 + 3 0 ∘ ∘ ∘ ∘ 2 ∘ without using a calculator.

  • A 1 1 1 2
  • B βˆ’ 1 2 1 1
  • C 1 2 1 1
  • D βˆ’ 1 1 1 2

Q14:

Find the value of 𝑋 in degrees given c o s 𝑋 = 1 2 where 𝑋 is an acute angle.

  • A 3 0 ∘
  • B 4 5 ∘
  • C 9 0 ∘
  • D 6 0 ∘

Q15:

Find the value of t a n t a n s i n c o s 6 0 ο€Ή 1 βˆ’ 4 5  3 0 6 0 ∘ 2 ∘ ∘ ∘ without using a calculator.

  • A βˆ’ 1
  • B1
  • C √ 3
  • D0
  • E 1 2

Q16:

Find πœƒ given s i n πœƒ = 1 2 and t a n πœƒ > 0 .

Q17:

Find the value of 3 3 0 6 0 βˆ’ 0 6 0 + 2 7 0 4 5 s i n s i n c o s s e c s i n c o s ∘ ∘ ∘ ∘ ∘ 2 ∘ .

  • A 1 0 + 3 √ 3 4
  • B βˆ’ 1 0 βˆ’ 3 √ 3 4
  • C 1 0 βˆ’ 3 √ 3 4
  • D βˆ’ 1 0 + 3 √ 3 4

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