Question

Тригонометрические формулы

Answer 1

3) 4 sin α = ?   cos α = $\frac{-3\sqrt{7} }{8}$    α ∈ (π; 3π/2) - 3-я четверть  (sin α < 0)

$sin^2\alpha = 1 - cos^2 \alpha = 1 - \dfrac{9\cdot7}{64} = \dfrac{1}{64}$

sin α = - 0.125

4sin α = -0.5

4) 21 cos γ = ?   sinγ = $\frac{-4\sqrt{3}}{7}$   γ ∈ (3π/2; 2π) - 4-я четверть (cos γ > 0)

$cos^2\gamma = 1 - sin^2 \gamma = 1 - \dfrac{16\cdot 3}{49} = \dfrac{1}{49}$

cos γ = 1/7

21 cos γ = 3

5)  tg α = ?   cos α = $\frac{2 \sqrt{29}}{29}$    α ∈  (3π/2; 2π) - 4-я четверть (tg α < 0)

$tg^2 \alpha = \dfrac{1}{cos^2 \alpha} -1 = \dfrac{1}{\dfrac{4}{29} }-1= \dfrac{29}{4}-1 = \dfrac{25}{4}$

tg α = - 2.5