Question

Given that tan θ ≈ 1.072, where 0 < θ < , 2 π find the values of sin θ and cos θ.

Answer 1

The answer to your question is

sin Ф = 0.731 and sinФ = -0.731; cos Ф 0.682 and cos Ф = -0.682

Explanation:

tan Ф = 1.072, 0 < Ф < 2 π, tan Ф is positive, find the solution in the first and third quadrangle.

- tan Ф = opposite side / adjacent side

- 1.072 / 1 = opposite side / adjacent side

- opposite side = 1.072 and adjacent side = 1

Calculate hypotenuse

c² = a² + b²

c² = 1.072² + 1²

c² = 2.149

hypotenuse = c = 1.466

First quadrangle

sin Ф = 1.072 / 1.466 = 0.731

cos Ф = 1 / 1.466 = 0.682

Third quadrangle

sin Ф = -1.072 / 1.466 = -0.731

cos Ф = -1 / 1.466 = -0.682