Question

Cos 29cos 119+sin 29sin119

Answer 1

Ответ:

Пошаговое объяснение:

=cos(29-119)=cos(-90)=0

Answer 2

To simplify the expression cos(29°)cos(119°) + sin(29°)sin(119°), we can use the angle addition formula for cosine:

cos(A + B) = cos(A)cos(B) - sin(A)sin(B)

In this case, A = 29° and B = 119°. So, the expression becomes:

cos(29° + 119°)

To find the value of cos(29° + 119°), we need to first determine the reference angle. Since 29° and 119° are both in the second quadrant (90° < angle < 180°), the reference angle can be found by subtracting the angle from 180°.

Reference angle for 29° = 180° - 29° = 151° Reference angle for 119° = 180° - 119° = 61°

Now, we have:

cos(29° + 119°) = cos(151°)

Since cos(151°) is negative in the second quadrant, we can use the value of the cosine function for the reference angle:

cos(151°) ≈ -0.866

So, the simplified value of the expression is approximately:

cos(29°)cos(119°) + sin(29°)sin(119°) ≈ -0.866