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Lesson: Evaluating Trigonometric Functions with Special Angles

In this lesson, we will learn how to use function values of special angles to evaluate trigonometric expressions.

Worksheet • 25 Questions

Q1:

Find the value of 5 ( 1 8 0 βˆ’ πœƒ ) βˆ’ 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 πœƒ = βˆ’ 4 c o s where 0 < πœƒ < 1 8 0 ∘ ∘ .

Q2:

Evaluate c o s c o s s i n s i n 5 5 4 5 β€² 7 9 1 5 β€² βˆ’ 5 5 4 5 β€² 7 9 1 5 β€² ∘ ∘ ∘ ∘ .

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

Q3:

Find the value of t a n 4 πœ‹ 3 .

  • A √ 3
  • B √ 2
  • C βˆ’ √ 3
  • D βˆ’ √ 2
  • E βˆ’ √ 3 3

Q4:

Find the value of t a n ο€» βˆ’ πœ‹ 3  .

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

Q5:

Find the value of s i n 7 πœ‹ 6 .

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

Q6:

Find t a n 3 0 ∘ .

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

Q7:

Evaluate s i n c o s c o s c o t 1 5 0 ( βˆ’ 2 4 0 ) + 2 1 3 0 2 4 0 ∘ ∘ ∘ ∘ .

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

Q8:

Find the value of t a n 7 πœ‹ 4 .

  • A βˆ’ 1
  • B √ 3
  • C1
  • D βˆ’ √ 2
  • E √ 2

Q9:

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

  • A 1 2
  • B βˆ’ 1
  • C βˆ’ 1 2
  • D1

Q10:

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

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

Q11:

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

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

Q12:

Calculate s i n c o s c o s s i n 2 4 0 3 3 0 βˆ’ 2 4 0 3 3 0 ∘ ∘ ∘ ∘ .

  • A βˆ’ 1
  • B 1 2
  • C1
  • D βˆ’ 1 2

Q13:

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

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

Q14:

Calculate s i n c o s c o s s i n 2 2 5 3 1 5 βˆ’ 3 0 0 2 1 0 ∘ ∘ ∘ ∘ .

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

Q15:

Calculate 4 3 3 0 2 4 0 βˆ’ 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 ∘ .

  • A βˆ’ 2
  • B βˆ’ 1
  • C1
  • D2

Q16:

Calculate 2 2 1 0 6 0 βˆ’ 9 0 6 0 + 9 0 2 2 5 s i n s i n c o s s e c s i n c o s ∘ 2 ∘ ∘ ∘ ∘ 2 ∘ .

  • A βˆ’ 1 4
  • B βˆ’ 5 4
  • C 5 4
  • D 1 4

Q17:

Calculate 2 3 3 0 3 0 0 βˆ’ 9 0 3 0 0 + 9 0 3 1 5 s i n s i n c o s s e c s i n c o s ∘ 2 ∘ ∘ ∘ ∘ 2 ∘ .

  • A βˆ’ 1 4
  • B βˆ’ 5 4
  • C 5 4
  • D 1 4

Q18:

Calculate 2 1 5 0 1 2 0 βˆ’ 2 7 0 1 2 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 ∘ ∘ ∘ ∘ 2 ∘ .

  • A 1 4
  • B 5 4
  • C βˆ’ 5 4
  • D βˆ’ 1 4

Q19:

Calculate 5 2 1 0 3 0 0 βˆ’ 2 7 0 3 0 0 + 2 7 0 2 2 5 s i n s i n c o s s e c s i n c o s ∘ 2 ∘ ∘ ∘ ∘ 2 ∘ .

  • A βˆ’ 1 9 8
  • B βˆ’ 1 1 8
  • C 1 1 8
  • D 1 9 8

Q20:

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

Q21:

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

  • A βˆ’ 1
  • B βˆ’ √ 2 + 1
  • C1
  • D βˆ’ 1 + √ 2

Q22:

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

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

Q23:

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

  • A √ 3 + 2
  • B2
  • C βˆ’ 2 βˆ’ √ 3
  • D βˆ’ 2

Q24:

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

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

Q25:

Find the value of s i n ο€» βˆ’ πœ‹ 6  .

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