Question

Найти sin(a+b) если sina=8/11 и sin бетта=15/17

Answer 1

Sin(a+b)=sinacosb+sinbcosa   в первой четверти синус и косинус положительны 

cosa=√(1-sin^2a)=√(1-64/289)=√(225/289)=15/17  

sinb=√(1-cos^2b)=√(1-16/25)=√(9/25)=3/5

sin(a+b)=8/17*4/5+3/5*15/17=32/85+45/85=77/85

Answer 2

To find the value of sin(a + b), we can use the trigonometric identity:

sin(a + b) = sin(a) * cos(b) + cos(a) * sin(b)

Given that sin(a) = 8/11 and sin(b) = 15/17, we need to find cos(a) and cos(b) to calculate sin(a + b). To do this, we can use the Pythagorean identity:

sin^2(x) + cos^2(x) = 1

Let's start by finding cos(a):

cos(a) = sqrt(1 - sin^2(a)) cos(a) = sqrt(1 - (8/11)^2) cos(a) = sqrt(1 - 64/121) cos(a) = sqrt(121/121 - 64/121) cos(a) = sqrt(57/121) cos(a) = sqrt(57)/11

Next, let's find cos(b):

cos(b) = sqrt(1 - sin^2(b)) cos(b) = sqrt(1 - (15/17)^2) cos(b) = sqrt(1 - 225/289) cos(b) = sqrt(289/289 - 225/289) cos(b) = sqrt(64/289) cos(b) = 8/17

Now, we have both cos(a) and cos(b). We can use these values to calculate sin(a + b):

sin(a + b) = sin(a) * cos(b) + cos(a) * sin(b) sin(a + b) = (8/11) * (8/17) + (sqrt(57)/11) * (15/17) sin(a + b) = (64/187) + (15 * sqrt(57))/187 sin(a + b) = (64 + 15 * sqrt(57))/187

So, the value of sin(a + b) is (64 + 15 * sqrt(57))/187.