If the final edge of angle θ passes through a point (- 1 / 2, √ 3 / 2), then the value of Tan θ is

If the final edge of angle θ passes through a point (- 1 / 2, √ 3 / 2), then the value of Tan θ is

The final edge of θ passes through the point (- 1 / 2, √ 3 / 2), its abscissa is x = - 1 / 2, and its ordinate is y = √ 3 / 2

The value of Tan (3 π - θ) is ()

Tan (2 π + π - θ) = Tan (π - θ) = - Tan θ (the multiple of π / 2 is even invariant and the second quadrant is negative)
TANθ=2/(-1)=-2 -TANθ=-(-2)=2
(Tan θ is the second quadrant, Tan (π - θ) is the first quadrant)

If Tan α = 1 / 3 and Tan (β - α) = - 2, then the value of Tan β is

tan（β-α）
=(tanβ-tanα)/(1+tanβtanα)
=(tanβ-1/3)/(1+tanβ/3)
=-2
So tan β - 1 / 3 = - 2 * (1 + Tan β / 3)
tanβ=-1

P (2, y) is a point on the final edge of an angle, and sin = - 1 / 3. Find the value of tan

According to the definition of trigonometric function,
Y / √ (4 + y squared) = - 1 / 3
∴①y＜0
② 9y squared = 4 + y squared
The solution is y = - 2 / 2 root 2
Tan α = Y / 2 = - 4 root 2

Given that π < α < 3 π / 2, 0 < β < π / 2, and Tan α = 1 / 7, cos β = √ 10 / 10, calculate the value of α + 2 β α + 2 β = 5 π / 4

cosβ=√10/10,0＜β＜π/2,
∴sinβ=(3√10）/10,tanβ=3,
tan2β=2*3/(1-9)=-3/4,
∴π/2

Given that Tan (α - β) = 1 / 7, Tan β = - 1 / 7, and α, β ∈ (π / 2,3 π / 2), find the value of 2 α - β

π/2

Given that Tan (a + β) = 1 / 7, Tan (a - β) = 1 / 3, calculate the value of Tan (a + 2 β)

The value of Tan (a + 2 β) = - 100

It is known that sin α + cos α = 7 13, α∈ (0, π), then Tan α is equal to () A. 12 Five B. −12 Five C. 5 Twelve D. −5 Twelve

∵sinα+cosα=7
13①
∴2sinαcosα=-120
169，
∴α∈（0，π），
∴α∈(π
2，π)，
∴sinα-cosα=17
13②
From ① and ②, sin α = 12
13，cosα＝−5
13，
∴tanα=-12
5，
Therefore, B is selected

Given that the coordinates of a point P on the final edge of the angle α are (- √ 3, y) and sin α = (√ 2 / 4) y, find cos α and Tan α

Because y: OP = sin α = y (radical 2 / 4)
So OP = 2 root sign 2
So | y | = radical (3 ^ 2 - (2 radical 2) ^ 2) = 1
So p (- radical 3, ± 1)
So cos α = radical 6 / 4
Tan α = ± radical 3 / 3

Given that the coordinates of a point P on the final edge of the angle α are (- √ 3, y) and sin α = (√ 3 / 4) y, calculate the values of cos α and Tan α

tanα=-y/√3
cosα=sinα/tanα=(√3/4)y/(-y/√3)=-3/4
(sinα)^2+(cosα)^2=1
sinα = √7/4,tanα = -√21/7,or,sinα = -√7/4,tanα = √21/7