Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Lesson: Finding the Values of the Three Trigonometric Ratios for an Angle

Video

12:12

Sample Question Videos

Worksheet • 14 Questions • 2 Videos

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 = 4 5 , c o s 𝐵 = 3 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 = 3 5 , c o s 𝐵 = 4 5 , t a n 𝐵 = 4 3

Q2:

Find the main trigonometric ratios of 𝐵 given 𝐴 𝐵 𝐶 is a right-angled triangle at 𝐶 where 𝐴 𝐵 = 4 0 c m and 𝐵 𝐶 = 3 2 c m .

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

Q3:

Find the main trigonometric ratios of 𝐵 given 𝐴 𝐵 𝐶 is a right-angled triangle at 𝐶 where 𝐴 𝐵 = 5 c m and 𝐵 𝐶 = 3 c m .

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

Q4:

Find the main trigonometric ratios of 𝐵 given 𝐴 𝐵 𝐶 is a right-angled triangle at 𝐶 where 𝐴 𝐵 = 3 5 c m and 𝐵 𝐶 = 2 8 c m .

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

Q5:

Find the main trigonometric ratios of 𝐵 given 𝐴 𝐵 𝐶 is a right-angled triangle at 𝐶 where 𝐴 𝐵 = 2 5 c m and 𝐵 𝐶 = 7 c m .

  • A s i n 𝐵 = 2 4 2 5 , c o s 𝐵 = 7 2 5 , t a n 𝐵 = 2 4 7
  • B s i n 𝐵 = 7 2 5 , c o s 𝐵 = 2 4 2 5 , t a n 𝐵 = 7 2 4
  • C s i n 𝐵 = 2 4 2 5 , c o s 𝐵 = 7 2 5 , t a n 𝐵 = 7 2 4
  • D s i n 𝐵 = 7 2 5 , c o s 𝐵 = 2 4 2 5 , t a n 𝐵 = 2 4 7

Q6:

𝐴 𝐵 is a diametre 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 = 3 5 and s i n 𝐵 = 3 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 = 4 5 and s i n 𝐵 = 4 5

Q7:

𝐴 𝐵 is a diametre of a circle with radius 48.5 cm. Point 𝐶 is on the circumference of the circle where 𝐴 𝐶 𝐶 𝐵 and 𝐴 𝐶 = 7 2 c m . Find the exact values of c o s 𝐴 and s i n 𝐵 .

  • A c o s 𝐴 = 7 2 9 7 and s i n 𝐵 = 7 2 9 7
  • B c o s 𝐴 = 6 5 9 7 and s i n 𝐵 = 7 2 9 7
  • C c o s 𝐴 = 7 2 9 7 and s i n 𝐵 = 6 5 9 7
  • D c o s 𝐴 = 6 5 9 7 and s i n 𝐵 = 6 5 9 7

Q8:

Find the main trigonometric ratios of given is a right triangle at where .

  • A , and
  • B , and
  • C , and
  • D , and

Q9:

Find the main trigonometric ratios of given is a right triangle at where .

  • A , and
  • B , and
  • C , and
  • D , and

Q10:

Find the main trigonometric ratios of given is a right triangle at where .

  • A , and
  • B , and
  • C , and
  • D , and

Q11:

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

Q12:

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 .

Q13:

Find given is a right triangle at where .

  • A
  • B
  • C
  • D

Q14:

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
Preview