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Question
From the following figure, find the values of:
- sin A
- cos A
- cot A
- sec C
- cosec C
- tan C
Solution
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`
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