Question

If 3sintheta-4costheta=0 find the value of tanyheta sectheta and cosectheta where theta is an acute angle​

Answer 1

Answer:

tan ∅ = 4/3, sec ∅ = 5/3, cosec ∅ = 5/4

[I am using this symbol (∅) for theta]

Step-by-step explanation:

3 sin∅ -4 cos∅ = 0

3 sin ∅ = 4 cos ∅

sin ∅/cos ∅ = 4/3

tan ∅ = 4/3

tan = perpendicular/base

so, perpendicular = 4

base = 3

using Pythagoras theorem we get,

AC² = AB² + BC²

AC² = 4² + 3²

AC² = 16 + 9

AC² = 25

AC = √25

AC = 5

So, tan ∅ = perpendicular/base

= 4/3

sec ∅ = hypotenuse/base

= 5/3

cosec ∅ = hypotenuse/perpendicular

= 5/4

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