Given that the final edge of the angle a passes through the point P (- √ 3, y) (Y ≠ 0) and sin a = √ 2 / 4 · y, find the values of COS A and Tan a

Given that the final edge of the angle a passes through the point P (- √ 3, y) (Y ≠ 0) and sin a = √ 2 / 4 · y, find the values of COS A and Tan a

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Given that there is a point P (3,4) on the final edge of the angle a, we can find sin a, cos A and Tan a respectively

tana=4/3 sina=4/√(4^2+3^2)=4/5 cosa=3/√(4^2+3^3)=3/5

If (- 4,3) is a point on the final edge of angle a, find the value of COS (A-3 π) * Tan (A-4 π) / sin (3 π - a) * cos (a + 5 π / 2)

(- 4,3) is a point on the final edge of angle A
obtain
A is the second quadrant angle
sina=3/5
cos(a-3π)=cos(a-3π+4π)=cos(a+π)=-cosa
tan(a-4π)=tana
sin(3π-a)=-sin(a-3π)=-sin(a-3π+4π)=-sin(a+π)=sina
cos(a+5π/2)=cos(a+5π/2-2π)=cos(a+π/2)=-sina
cos(a-3π)*tan(a-4π)/sin(3π-a)*cos(a+5π/2)
=[(-cosa)tana]/[sina*(-sina)]
=-sina/-sin²a
=1/sina
=5/3

Given cos α = 5 / (13) and (3 π) / 2 < α < 2 π, what is tan α equal to?

From the range of α, α is in the fourth quadrant, so sin α = --1 -- (5 / 13) 2 = -- 12 / 13, so tan α = sin α / cos α = -- (12 / 13) / 5 / 13 = - 12 / 5

If cos (α + β) = - 1 and Tan α = 2, then Tan β is equal to () A. 2 B. 1 Two C. -2 D. −1 Two

Because cos (α + β) = - 1,  sin (α + β) = 0,  Tan (α + β) = 0,  Tan α + Tan β
1−tanα•tanβ=0，
Tan α = 2,  Tan β = - 2,
Therefore, C

If the final edge of the angle a passes through the point P (- 3,4), then sin a + cos a + Tan A is equal to?

x=-3,y=4
r=√(x²+y²)=5
So the original formula = Y / R + X / R + Y / x = - 17 / 15

If cos α = - 4 / 5 and α belongs to (π / 2, π), then Tan (π / 4 - α) is equal to?

α belongs to (π / 2, π), and sin α is more than 0 ᚠ sin α = (1-cos 2 ᛿ α) = (1-16 / 25) = 3 / 5 ɉ Tan α = sin α / cos α = (3 / 5) / (- 4 / 5) = - 3 / 4 ᛽ Tan (π / 4-α) = [Tan (π / 4) Tan α] / [1 + Tan (π / 4) Tan α] = (1-tan α) / (1 + Tan α) = (1 + 3 / 4 / 4) = (1 + 3 / 4 / 4) = (1 + 3 / 4 / 4) = (1 + 3 / 4 / 4) 4 = 1 + 3 / 4 / 4) Tan α = (1-tan α) / (1-tan α)) / (1

If α∈ (π, 2 / 3 π), cos α = - 4 / 5, then Tan (π / 4 - α) is equal to?

Because α∈ (π, 2 / 3 π), cos α = - 4 / 5
So sin α

It is known that cos θ = - 3 5，θ∈（π 2, π), then Tan θ is equal to () A. 4 Three B. 3 Four C. −4 Three D. −3 Four

∵cosθ=-3
5，θ∈（π
2，π），
∴sinθ=
1−cos2θ=4
5，
Then Tan θ = sin θ
cosθ=-4
3．
Therefore, C

Then cos α is equal to 3?

Cosa = (1-tan square A / 2) / (1 + Tan square A / 2)
=(1-9)/(1+9)
=-4/5