Question

From the following figure, find the values of:

1. sin A
2. cos A
3. cot A
4. sec C
5. cosec C
6. tan C

Answer 1

Given angle  ABC = 90°

⇒ AC²  = AB² + BC²         ...(AC is hypotenuse)

⇒ AC² = 3² + 4² 

∴ AC² = 9 + 16 

∴ AC² = 25

∴ AC² = `sqrt25`

∴ AC = 5

(i) sin A = `" perpendicular"/" hypotenuse" = "BC"/ "AC" = 4/5`

(ii) cos A = `"base"/"hypotenuse" = "AB"/ "AC" = 3/5`

(iii) cot A = `"base "/"perpendicular" = "AB"/ "BC" = 3/4`

(iv) sec C = `"hypotenuse "/"base" = "AC"/ "BC" = 5/4`

(v) cosec C = `"hypotenuse"/" perpendicular" = "AC"/ "AB" = 5/3`

(vi) tan C = `" perpendicular"/"base" = "AB"/ "BC" = 3/4`