Evaluate sin16° cos29° + cos16° sin29°
This is what it is about:
http://www.youtube.com/watch?v=zw0waJCEc-w
sin 45 = (1/2)sqrt 2
Did you notice 16+29 = 45 ?
so
sin16° cos29° + cos16° sin29°
= sin(16+29)
= sin 45
= 1/√2 or √2/2
To evaluate sin16° cos29° + cos16° sin29°, we can use the trigonometric identity:
sin(A + B) = sinA cosB + cosA sinB
By substituting A = 16° and B = 29°, we have:
sin(16° + 29°) = sin16° cos29° + cos16° sin29°
Now, we can evaluate the sum of the angles, which gives:
sin(45°) = sin16° cos29° + cos16° sin29°
Since sin(45°) is equal to √2/2, we can rewrite the equation as:
√2/2 = sin16° cos29° + cos16° sin29°
Therefore, the final evaluation of sin16° cos29° + cos16° sin29° is √2/2.
To evaluate the expression sin(16°)cos(29°) + cos(16°)sin(29°), we can use the trigonometric identity for the sum of two angles:
sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
In this case, A = 16° and B = 29°. Using the identity, we can rewrite the expression as:
sin(16° + 29°)
Now, we can simplify the angle:
16° + 29° = 45°
So the expression becomes:
sin(45°)
Using the trigonometric identity sin(45°) = √2/2, we can evaluate the expression:
sin(45°) = √2/2
Therefore, sin(16°)cos(29°) + cos(16°)sin(29°) = √2/2.