Question

if 4tanQ=3, evaluate (4sinQ-cosQ+1)and (4sin Q + cosQ -1)

Answer 1

4tanQ = 3 so, tanQ = 3/4

we know, tanQ = perpendicular/base
tanQ = 4/3 = perpendicular/base
So, perpendicular = 3 and base = 4
Now use Pythagoras theorem to find hypotenuse
Hypotenuse = √{perpendicular ²+base²}
∴ hypotenuse = √(3² + 4²) = √(25) = 5

Now, sinQ = perpendicular/hypotenuse = 3/5
cosQ = base/hypotenuse = 4/5

now, (4sinQ - cosQ + 1)
= 4 × 3/5 - 4/5 + 1
= 12/5 - 4/5 + 1
= 8/5 + 1
= 1.6 + 1
= 2.6

Hence, (4sinQ - cosQ + 1) = 2.6

now,(4sinQ+cosQ-1)=4×3/5+4/5-1
=12/5 + 4/5 - 1
=16/5 - 1
=11/5=2.2