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Lesson: Evaluating Trigonometric Functions Using Pythagorean Identities

Sample Question Videos

Worksheet • 22 Questions • 2 Videos

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

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

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

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 .

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

Q6:

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

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

Q7:

Find s i n 𝐴 , given 𝐴 𝐡 𝐢 is a right-angled triangle at 𝐡 where c o s 𝐴 = 0 . 8 .

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

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

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 βˆ’ √ 1 3 6
  • B 1 3 3 6
  • C βˆ’ 6 √ 1 3
  • D 6 √ 1 3
  • E √ 1 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 1 3 1 2
  • B βˆ’ 1 3 1 2
  • C 1 2 1 3
  • D βˆ’ 1 2 1 3

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

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

Q14:

Find the value of c s c s i n t a n c s c πœƒ πœƒ βˆ’ πœƒ πœƒ given πœƒ ∈  πœ‹ 2 , πœ‹  and c o s πœƒ = βˆ’ 4 5 .

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

Q15:

Find the value of c s c s i n t a n c o t c o s πœƒ πœƒ βˆ’ πœƒ πœƒ + πœƒ 2 given πœƒ ∈  0 , πœ‹ 2  and s i n πœƒ = 2 0 2 9 .

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

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

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

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