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Worksheet: Evaluating Trigonometric Expressions Using Double-Angle Identities

Q1:

Find the value of 2 8 1 1 1 5 1 1 1 5 2 2 3 0 s i n c o s c o s .

  • A 7 2
  • B 1 7 2
  • C 1 7 2
  • D 7 2

Q2:

Find the value of given where .

  • A
  • B
  • C
  • D

Q3:

Find the value of c o s 𝜃 2 given s i n 𝜃 = 3 5 where 0 < 𝜃 < 9 0 .

  • A 5 3 4 3 4
  • B 1 0 1 0
  • C 2 5 5
  • D 3 1 0 1 0

Q4:

Find the value of c o s ( 2 𝐴 + 9 0 ) given 5 𝐴 = 1 2 t a n where 2 7 0 < 𝐴 < 3 6 0 .

  • A 1 1 9 1 6 9
  • B 1 2 0 1 6 9
  • C 1 1 9 1 6 9
  • D 1 2 0 1 6 9

Q5:

Find, without using a calculator, t a n 2 𝐴 given c o s 𝐴 = 9 1 5 where 0 < 𝐴 < 9 0 .

  • A 8 2 1
  • B 1 2 7
  • C 2 1 6 7
  • D 2 4 7

Q6:

Find the value of s i n 𝜃 2 given s i n 𝜃 = 8 1 7 where 1 8 0 < 𝜃 < 2 7 0 .

  • A 2 5 5
  • B 1 7 1 7
  • C 5 5
  • D 4 1 7 1 7

Q7:

Find the value of s i n 2 𝐴 given c o s 2 𝐴 = 9 2 5 where 𝐴 𝜋 , 3 𝜋 2 .

  • A 8 5
  • B 1 2 2 5
  • C 2 4 2 5
  • D 2 4 2 5
  • E 1 2 2 5

Q8:

Find the value of t a n 2 2 3 0 without using a calculator.

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

Q9:

Find the value of c o s 𝐴 given c o s ( 2 𝐴 ) = 7 2 5 where 𝐴 is a positive acute angle.

  • A 5 3
  • B 4 5
  • C 5 4
  • D 3 5

Q10:

Find the value of s i n 𝜃 2 given c o s 𝜃 = 1 2 1 3 where 9 0 < 𝜃 < 1 8 0 without using a calculator.

  • A 1 0 1 0
  • B 2 6 2 6
  • C 5 5
  • D 5 2 6 2 6

Q11:

Find the value of given where .

  • A
  • B
  • C
  • D
  • E

Q12:

Find the value of c o s 1 5 without using a calculator.

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

Q13:

Find the value of given where and where .

  • A
  • B
  • C
  • D
  • E

Q14:

Find, without using a calculator, the value of s i n 2 𝐴 given c o t 𝐴 = 2 0 2 1 where 0 < 𝐴 < 𝜋 2 .

  • A 4 1 8 4 1
  • B 4 2 0 8 4 1
  • C 4 0 0 8 4 1
  • D 8 4 0 8 4 1

Q15:

Find, without using a calculator, the value of s i n 2 𝐴 given c s c 𝐴 = 5 3 where 2 7 0 < 𝐴 < 3 6 0 .

  • A 7 2 5
  • B 1 2 2 5
  • C 7 2 5
  • D 2 4 2 5

Q16:

Find, without using a calculator, the value of t a n 2 𝐴 given s i n 𝐴 = 2 4 2 5 , where 0 < 𝐴 < 9 0 .

  • A 4 8 5 2 7
  • B 1 6 8 5 2 7
  • C 2 3 5 2 5 2 7
  • D 3 3 6 5 2 7

Q17:

Find, without using a calculator, the value of c o s 2 𝐴 given t a n 𝐴 = 3 4 where 𝜋 < 𝐴 < 3 𝜋 2 .

  • A 7 2 5
  • B 2 4 2 5
  • C 2 4 2 5
  • D 7 2 5

Q18:

Find the value of 2 1 5 7 3 0 1 c o s 2 without using a calculator.

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

Q19:

Find the value of 2 6 7 3 0 1 c o s 2 without using a calculator.

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

Q20:

Find s i n 2 𝑎 given c o s s i n 𝑎 𝑎 = 1 1 2 .

  • A 1 1 4 4
  • B 1 1 1 2
  • C 1 2 8 8
  • D 1 4 3 1 4 4

Q21:

Find, without using a calculator, the value of c o s 𝜃 2 given t a n 𝜃 = 4 3 where 𝜋 < 𝜃 < 3 𝜋 2 .

  • A 2 5 5
  • B 2 5 5
  • C 5 5
  • D 5 5

Q22:

Evaluate c o s s i n 2 2 1 6 5 1 6 5 without using a calculator.

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

Q23:

Find the value of s i n 2 𝑋 given s i n c o s 𝑋 + 𝑋 = 1 3 .

  • A 1 9
  • B 2 3
  • C 1 3
  • D 2 3
  • E 1 3

Q24:

Find, without using a calculator, the value of c o s 2 𝐴 given c s c 𝐴 = 5 3 where 0 < 𝐴 < 9 0 .

  • A 4 3 2 5
  • B 2 4 2 5
  • C 1 6 2 5
  • D 7 2 5

Q25:

Evaluate c o s s i n 4 4 1 1 2 3 0 1 1 2 3 0 without using a calculator.

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