Question

Вычислить sina,tga,cos2a, если cosa= -4/5 , п/2<а<п

Answer 1

cosa= -4/5 , п/2<а<п, sin a>0, tg a<0
cos^2(a)=16/25
cos^2(a)=1-sin^2(a)
sin^2(a)=1-cos^2(a)=1-16/25=9/25
sina=3/5
tga=sina/cosa=(3/5)/(-4/5)= -3/4
cos(2a)=cos^2(a)-sin^2(a)=16/25-9/25=7/25

Answer 2

To calculate the values of sine (sin a), tangent (tan a), and cosine squared (cos^2 a) given that cos a = -4/5 and π/2 < a < π, we can use trigonometric identities.

First, let's find the value of sin a using the identity: sin^2 a + cos^2 a = 1

sin^2 a = 1 - cos^2 a

sin^2 a = 1 - (-4/5)^2

sin^2 a = 1 - 16/25

sin^2 a = (25 - 16) / 25

sin^2 a = 9 / 25

sin a = ± √(9/25) = ± 3/5

Since π/2 < a < π, the angle a lies in the second quadrant where sine is positive. So, sin a = 3/5.

Next, let's find the value of tan a using the identity: tan a = sin a / cos a

tan a = (3/5) / (-4/5)

tan a = (3/5) * (-5/4)

tan a = -3/4

Finally, let's find the value of cos^2 a directly since we already know cos a = -4/5:

cos^2 a = (-4/5)^2

cos^2 a = 16/25

Now, we have the following values:

sin a = 3/5 tan a = -3/4 cos^2 a = 16/25

Please note that the value of cos a being negative means the angle a is in the second quadrant or third quadrant, and we need to consider the appropriate sign for sin a. In this case, sin a is positive in the second quadrant.