Question

Sin83 *cos 67 +cos 83*sin 67

Answer 1

Sin83cos67+cos83sin67=sin(83+67)=sin150=sin(180-30)=sin30=0.5

Answer 2

To calculate the expression sin(83) * cos(67) + cos(83) * sin(67), you can use the trigonometric identities:

1. sin(a) * cos(b) = (1/2) * [sin(a + b) + sin(a - b)]
2. cos(a) * sin(b) = (1/2) * [sin(a + b) - sin(a - b)]

Let's apply these identities to the given expression:

sin(83) * cos(67) + cos(83) * sin(67) = (1/2) * [sin(83 + 67) + sin(83 - 67)] + (1/2) * [sin(83 + 67) - sin(83 - 67)] = (1/2) * [sin(150) + sin(16)] + (1/2) * [sin(150) - sin(16)]

Now, we know that sin(150°) = 1/2 and sin(16°) ≈ 0.2756374.

Substitute these values back into the equation:

= (1/2) * [1/2 + 0.2756374] + (1/2) * [1/2 - 0.2756374] = (1/2) * [0.7756374] + (1/2) * [0.2243626] = 0.7756374/2 + 0.2243626/2 = 0.3878187 + 0.1121813 = 0.5

So, sin(83) * cos(67) + cos(83) * sin(67) is equal to 0.5.