If cos θ = 4 / 5, and 3 π / 2 〈θ〈 2 π, then Tan θ / 2 =?

If cos θ = 4 / 5, and 3 π / 2 〈θ〈 2 π, then Tan θ / 2 =?

Because Tan θ / 2 = sin θ / 2 / cos θ / 2 = (2Sin θ / 2cos θ / 2) / (2cos θ / 2cos θ / 2) = sin θ / (1 + cos θ) because cos θ = 4 / 5,3 π / 2

If cos α = - (4 / 5), and 2 α belongs to ((3 π / 20,2 π), what is tan α equal to

From what is known
Because 2 α belongs to (3 π / 20,2 π), α belongs to (3 π / 40, π) and cos α = - (4 / 5), so sin α = (3 / 5)
So tan α = sin α / cos α = - (3 / 4)

If cos α = - 4 / 5, α∈ the third quadrant, then (1 + Tan α / 2) / (1-tan α / 2) =? As the title

Because alpha is the third quadrant angle, sin alpha

If (sin α + cos α) / (sin α - cos α) = 2, then sin (α - 5 π) · sin (3 π / 2 - α) =?

From (sin α + cos α) / (sin α - cos α) = 2, Sina = 3cosa, and sin? 2A + cos? A = 1, so cos? 2A = 1 / 10
So sin (α - 5 π) · sin (3 π / 2 - α) = - Sina (- COSA) = sinacosa = 3cos? A = 3 / 10

Let cos (α - β / 2) = - 3 / 5, sin (α / 2 - β) = 2 / 3, and π / 2 < α < π, 0 < β < π / 2, find cos (α + β)

Under known conditions, it is obtained that - π / 4 < α / 2 - β < π / 2, ∵ sin (α / 2 - β) > 0 ᙽ 0 < α / 2 - β < π / 2, cos (α / 2 - β) = √ 5 / 3
π/4<α-β/2<π,∵cos（α-β/2）<0,∴π/2<α-β/2<π,sin（α-β/2）=4/5
cos（α/2+β/2)=cos[(α-β/2)-(α/2-β)]=(8-3√5)/15
cos(α+β)=2cos2（α/2+β/2)-1
=-(96√5+7)/225

(sin θ + cos θ) / (sin θ - cos θ) = 2, then sin (θ - 5 π) * sin (3 π / 2 - θ)=

(sinθ + cos θ) / (sinθ - cos θ) = 2Sin θ + cos θ = 2Sin θ + cos θ = 2Sin θ - 2cos θ 3cos θ = sin θ = sin θ = sin θ = sin θ = 2 = 9 cos ^ 2 ^ 2 θ = 1-cos ^ 2 θ = 1-cos ^ 2 θ = 1 / 10 | cos θ | = 1 / root number 10 | sin θ | = 3 | cos θ| = 3 | cos | 2 | cos | 2 | cos ^ 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 124a = 3 / radical 10sin (θ - 5 π) * sin (

If cos α = 3 / 5 and α∈ (3 Π / 2,2 Π), then cos (α - Π / 3)=

Because α ∈ (3 Π / 2,2 Π), that is, α is in the fourth quadrant, so sin α = - 4 / 5,
Therefore, cos (α - Π / 3) = 1 / 2cos α + √ 3 / 2Sin α = (3-4 √ 3) / 10

Given that cos θ is equal to minus 3 / 5 and θ belongs to (π, 3 / 2 π), calculate the value of θ of Cos2

∵ θ ∈ (π, 3 π / 2), then θ / 2 ∈ (π / 2,3 π / 4)  cos θ / 2 < 0 ﹤ cos θ = 2cos θ / 2-1 = - 3 / 5 cos θ / 2 = 1 / 5 ﹤ cos θ / 2 = - √ 5 / 5

What is π three times of COS equal to

cos(π/3)=1/2 sin(π/3)=√3/2 tan(π/3)=√3 cot(π/3)=√3/3

It is known that cos (5 π / 12 + a) = 1 / 3 and - π

cos(π/12-a)
=sin[π/2-(π/12-a)]
=sin(5π/12 +a)
π - Dang