Question

find sinØ if 3 cosØ+4 sinØ=4​

Answer 1

A᭄nswer:

sin∅ = 1 or sin∅ = 7/25

Step-by-step explanation:

We'll substitute sin∅ = x for easy calculation.

Then cos∅ = √(1sin²∅) = √(1-x²)

Now giving equation

3cos∅ + 4sin∅ = 4

3cos∅ = 4-4sin∅

3√(1-x²)=4(1-x)

Squaring both side,

9(1-x²) = 16(1-2x+x²)

9-9x² = 16-32x+16x²

25x²-32x+7 = 0

Solving this quadratic eqn

x = 1 or x = 7/25

sin∅ = 1 or sin ∅ = 7/25

Hence,the value of sin∅ can be either 1 or 7/25.