Question

Если sinA=-40/41,tgB=9/40,A∈Ⅳч,то чему равен tg(a+b)

Answer 1

sinα = -40/41; tgβ = 9/40

cosα = √(1 - cos²α) = √(1 - 40²/41²) = √((41² - 40²)/41²) = √((81)/41²) = 9/41;

tgα = sinα/cosα = -40/9

tg(α+β) = (tgα + tgβ)/(1 - tgα · tgβ) = (-40/9 + 9/40)/(1 + 40/9 · 9/40) = -1519/(2 · 360) = -1519/720

Answer 2

Sina=-40/41
tgb=9/40 ;a€|V
tg(a+b)=(tga+tgb)/(1-tga*tgb)=?

cos²a=1-sin²a=1-1600/1681=81/1681
cosa=9/41;a€|V

tga=sina/cosa=-40/41:9/41=-40/9
tg(a+b)=(-40/9+9/40)(1+9/40*40/9)
=(-1600+81)/(2*360)=
-1519/720

Answer 3

To find the value of tg(a + b), we can use trigonometric identities to relate the trigonometric functions of angles A and B. First, let's recall the definitions of sin, cos, and tan for a given angle:

sin(A) = opposite / hypotenuse cos(A) = adjacent / hypotenuse tan(A) = opposite / adjacent

Given that sin(A) = -40/41 and A is in the fourth quadrant (IV четверть), we can construct a right-angled triangle in the fourth quadrant, where the opposite side is -40 and the hypotenuse is 41 (since both sin and cos are negative in the fourth quadrant).

Now, we can use the Pythagorean theorem to find the adjacent side:

adjacent^2 = hypotenuse^2 - opposite^2 adjacent^2 = 41^2 - (-40)^2 adjacent^2 = 1681 - 1600 adjacent^2 = 81 adjacent = √81 adjacent = 9

So, cos(A) = adjacent / hypotenuse = 9 / 41.

Next, we are given that tan(B) = 9/40. We can set up another right-angled triangle in the first quadrant (I четверть) where the opposite side is 9 and the adjacent side is 40.

Now, let's find the value of tan(A + B) using the tangent addition formula:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A) * tan(B))

We already know that tan(A) = sin(A) / cos(A) and we have values for sin(A), cos(A), and tan(B).

tan(A) = -40/41 / 9/41 = -40/9

Now, let's plug these values into the tangent addition formula:

tan(A + B) = (-40/9 + 9/40) / (1 - (-40/9) * (9/40)) tan(A + B) = (-40/9 + 9/40) / (1 + 1) tan(A + B) = (-1600 + 81) / 360 tan(A + B) = -1519 / 360

To simplify the fraction further, we can divide both the numerator and denominator by their greatest common divisor (GCD):

GCD(1519, 360) = 1 tan(A + B) = -1519 / 360

Therefore, tg(a + b) is equal to -1519 / 360.