Question

Given that tan theta = 3 / 4, find; (1) cos theta and
(2)sine if 0 less than or equal to theta less than lor equal to 90degrees

Answer 1

Answer:

4/5 and 3/5

Step-by-step explanation:

Since 0<θ<90, both sinθ and cosθ will also be positive.

Now Tanθ = opposite side to θ/Adjacent side to θ.

Imagine a right angled triangle, with right angled at B and ∠c = θ.

So Opposite side to θ = Height of the triangle and adjacent side = base of the triangle.

Using Pythagoras theorem,

Hypotenuse ² = height² + Base²

Hypotenuse = √ (3)² + (4)² = √25 = 5 (∵Since 0<θ<90)

Sinθ = opposite side to θ/Hypotenuse = 3/5.

Cosθ = Adjacent side to θ/Hypotenuse = 4/5