Question

TgA=0.75 CosA=? SinA=?

Answer 1

sinA=±3/5

cosA=±4/5

cosA=✓1/1+(tgA)^2

sinA=tgAcosA

Answer 2

To find the values of cosine (cos) and sine (sin) for angle A, given that the tangent (tg) of angle A is 0.75, we can use the following trigonometric identities:

1. cos^2(A) + sin^2(A) = 1
2. tan(A) = sin(A) / cos(A)

Given that tan(A) = 0.75, we can substitute this value into equation (2):

0.75 = sin(A) / cos(A)

Now, we can solve for sin(A) and cos(A) using algebraic manipulation:

sin(A) = 0.75 * cos(A) (multiplying both sides by cos(A))

Now, we can substitute this value of sin(A) into equation (1):

cos^2(A) + (0.75 * cos(A))^2 = 1

Expanding and simplifying:

cos^2(A) + 0.5625 * cos^2(A) = 1

1.5625 * cos^2(A) = 1

cos^2(A) = 1 / 1.5625

cos^2(A) = 0.64

Taking the square root of both sides:

cos(A) = ±√0.64

cos(A) = ±0.8

Since cosine is positive in the first and fourth quadrants, we take the positive value:

cos(A) = 0.8

Now, we can substitute this value of cos(A) into the equation for sin(A):

sin(A) = 0.75 * cos(A)

sin(A) = 0.75 * 0.8

sin(A) = 0.6

Therefore, for angle A, we have:

cos(A) = 0.8 sin(A) = 0.6