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Worksheet: Using Pythagorean Identities to Evaluate Trigonometric Functions

Q1:

Find c o s πœƒ given s i n πœƒ = βˆ’ 3 5 where 2 7 0 ≀ πœƒ < 3 6 0 ∘ ∘ .

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

Q2:

Find t a n πœƒ given s i n πœƒ = βˆ’ 3 5 where 2 7 0 ≀ πœƒ < 3 6 0 ∘ ∘ .

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

Q3:

Find c o t πœƒ given s i n πœƒ = 3 5 where 9 0 < πœƒ < 1 8 0 ∘ ∘ .

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

Q4:

Find the value of t a n ( 3 6 0 βˆ’ πœƒ ) ∘ given c o t πœƒ = 4 3 where 0 < πœƒ < 9 0 ∘ ∘ .

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

Q5:

Find the value of s i n c o s πœƒ πœƒ given s i n c o s πœƒ + πœƒ = 5 4 where 0 < πœƒ < πœ‹ 2 .

  • A 1 8
  • B 9 1 6
  • C 1 3 2
  • D 9 3 2

Q6:

Find the value of c o t 2 πœƒ given c s c 2 πœƒ = 2 5 9 .

  • A 9 1 6
  • B 4 3
  • C 1 6 2 5
  • D 1 6 9

Q7:

Find , given is a right triangle at where .

  • A
  • B
  • C
  • D
  • E

Q8:

Find the value of s e c πœƒ given s e c t a n πœƒ βˆ’ πœƒ = 1 6 where 0 < πœƒ < πœ‹ 2 .

  • A 2 0 9
  • B 3 5 1 2
  • C 3 7 1 8
  • D 3 7 1 2

Q9:

Find the value of 1 7 πœƒ + 9 πœƒ + 8 πœƒ s i n c o s s e c 2 2 2 .

Q10:

Knowing that s i n π‘₯ = √ 1 3 7 and πœ‹ 2 ≀ π‘₯ ≀ πœ‹ , find t a n π‘₯ .

  • A √ 1 3 6
  • B βˆ’ 6 √ 1 3
  • C 6 √ 1 3
  • D βˆ’ √ 1 3 6
  • E 1 3 3 6

Q11:

Find the value of s e c ( βˆ’ πœƒ ) given c s c πœƒ = 1 3 5 where 0 < πœƒ < 9 0 ∘ ∘ .

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

Q12:

Find the value of t a n ( 1 8 0 + πœƒ ) ∘ given s i n πœƒ = 3 5 where 0 < πœƒ < 9 0 ∘ ∘ .

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

Q13:

Find the value of s i n πœƒ given c o s πœƒ = βˆ’ 2 1 2 9 where 9 0 < πœƒ < 1 8 0 ∘ ∘ .

  • A 2 0 2 1
  • B βˆ’ 2 0 2 9
  • C 2 1 2 9
  • D 2 0 2 9
  • E βˆ’ 2 0 2 1

Q14:

Find the value of given and .

  • A
  • B
  • C
  • D

Q15:

Find the value of given and .

  • A
  • B
  • C
  • D

Q16:

Find the value of 2 πœƒ πœƒ s i n c o s given 1 2 πœƒ + 5 = 0 t a n where 1 8 0 < πœƒ < 3 6 0 ∘ ∘ .

  • A 5 2 4
  • B 1 2 0 1 6 9
  • C βˆ’ 5 2 4
  • D βˆ’ 1 2 0 1 6 9

Q17:

Find the value of 2 πœƒ πœƒ s i n c o s given 3 πœƒ + 4 = 0 t a n where 0 < πœƒ < 2 7 0 ∘ ∘ .

  • A 2 3
  • B 2 4 2 5
  • C βˆ’ 2 3
  • D βˆ’ 2 4 2 5

Q18:

Find 1 + 𝐴 t a n 2 , given 𝐴 𝐡 𝐢 is a right-angled triangle at 𝐢 where 𝐴 𝐡 = 1 0 c m and 𝐡 𝐢 = 6 c m .

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

Q19:

Find c s c s e c π‘Ž βˆ’ π‘Ž given c o s s i n π‘Ž βˆ’ π‘Ž = 2 7 .

  • A βˆ’ 2 8 4 5
  • B 1 4 4 5
  • C βˆ’ 4 5 1 4
  • D 2 8 4 5

Q20:

Simplify s i n s i n 2 2 ∘ ( πœ‹ βˆ’ πœƒ ) + ( 2 7 0 βˆ’ πœƒ ) .

Q21:

Simplify s i n s i n 2 2 ∘ πœƒ + ( 9 0 βˆ’ πœƒ ) .

Q22:

Find s e c t a n πœƒ βˆ’ πœƒ given s e c t a n πœƒ + πœƒ = βˆ’ 1 4 2 7 .

  • A 4 1 1 4
  • B 2 7 1 4
  • C βˆ’ 4 1 1 4
  • D βˆ’ 2 7 1 4