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Worksheet: Trigonometric Ratios in Right Triangles

Q1:

Find the main trigonometric ratios of 𝐵 given 𝐴 𝐵 𝐶 is a right-angled triangle at 𝐶 where 𝐴 𝐵 = 3 0 c m and 𝐵 𝐶 = 1 8 c m .

  • A s i n 𝐵 = 3 5 , c o s 𝐵 = 4 5 , t a n 𝐵 = 4 3
  • B s i n 𝐵 = 3 5 , c o s 𝐵 = 4 5 , t a n 𝐵 = 3 4
  • C s i n 𝐵 = 4 5 , c o s 𝐵 = 3 5 , t a n 𝐵 = 3 4
  • D s i n 𝐵 = 4 5 , c o s 𝐵 = 3 5 , t a n 𝐵 = 4 3

Q2:

𝐴 𝐵 is a diameter of a circle with radius 62.5 cm. Point 𝐶 is on the circumference of the circle where 𝐴 𝐶 𝐶 𝐵 and 𝐴 𝐶 = 7 5 c m . Find the exact values of c o s 𝐴 and s i n 𝐵 .

  • A c o s 𝐴 = 4 5 and s i n 𝐵 = 4 5
  • B c o s 𝐴 = 4 5 and s i n 𝐵 = 3 5
  • C c o s 𝐴 = 3 5 and s i n 𝐵 = 4 5
  • D c o s 𝐴 = 3 5 and s i n 𝐵 = 3 5

Q3:

Find the main trigonometric ratios of 𝐶 given 𝐴 𝐵 𝐶 is a right-angled triangle at 𝐵 where 2 0 𝐴 = 2 1 t a n .

  • A s i n 𝐶 = 2 0 2 9 , c o s 𝐶 = 2 1 2 9 and t a n 𝐶 = 2 1 2 0
  • B s i n 𝐶 = 2 1 2 9 , c o s 𝐶 = 2 0 2 9 and t a n 𝐶 = 2 0 2 1
  • C s i n 𝐶 = 2 1 2 9 , c o s 𝐶 = 2 0 2 9 and t a n 𝐶 = 2 1 2 0
  • D s i n 𝐶 = 2 0 2 9 , c o s 𝐶 = 2 1 2 9 and t a n 𝐶 = 2 0 2 1

Q4:

Find the value of c o s s i n 2 2 𝑥 5 + 𝑥 5 .

Q5:

Find 𝑥 in the given figure. Give your answer to two decimal places.

Q6:

Find 𝑚 𝐵 given 𝐴 𝐵 𝐶 is a triangle where 𝑚 𝐴 = 1 1 1 and s i n c o s 𝐶 = 𝐶 .

Q7:

Find given is a right-angled triangle at where .

Q8:

Find c o t 𝛼 given 𝐴 𝐵 𝐶 𝐷 is a rectangle where t a n 𝜃 = 1 0 1 7 and 𝐵 𝐹 𝐴 𝐸 .

  • A 1 0 1 7
  • B 1 7 1 0
  • C 1 7 1 0
  • D 1 0 1 7

Q9:

Find the value of 3 1 𝜃 + 2 6 𝜃 s i n c o s 2 2 .

  • A 5 7 + 𝜃 c o s 2
  • B 2 6 + 5 𝜃 c o s 2
  • C 5 7 + 𝜃 s i n 2
  • D 2 6 + 5 𝜃 s i n 2

Q10:

Find the value of c s c ( 2 7 0 𝜃 ) given s i n ( 9 0 𝜃 ) = 1 7 2 0 where 𝜃 is the smallest positive angle.

  • A 2 0 1 1 1
  • B 2 0 1 7
  • C 2 0 1 1 1
  • D 2 0 1 7

Q11:

Find the value of 7 1 6 5 + 7 1 6 5 c o s s i n 2 2 .

Q12:

Simplify ( 𝜃 + 𝜃 ) 2 𝜃 𝜃 s i n c o s s i n c o s 2 .

Q13:

Simplify s i n c o s s i n c o s 4 4 2 2 𝜃 𝜃 𝜃 𝜃 .

Q14:

Find the value of ( 𝑥 + 𝑥 ) + ( 𝑥 𝑥 ) c o s s i n c o s s i n 2 2 .