Question

Please please help me! This is due ASAP

sin 200 degrees cos 80 degrees- cos 200 degrees sin 80 degrees

Thank you!!

Answer 1

Answer: -sqrt(3)/4

Explanation:

To solve this trigonometric expression, we can use the following trigonometric identities:

sin (180 + x) = -sin x

cos (180 + x) = -cos x

Using these identities, we can rewrite the expression as:

sin(200°)cos(80°) - cos(200°)sin(80°)

= sin(180° + 20°)cos(80°) - cos(180° + 20°)sin(80°)

= -sin(20°)cos(80°) + cos(20°)sin(80°)

= (cos(20°) - sin(20°))sin(80°)

= sin(70°)sin(80°)

= (cos(20°) - cos(150°))/2

= (-sqrt(3)/2 - sqrt(3)/2)/2

= -sqrt(3)/4

Therefore, sin(200°)cos(80°) - cos(200°)sin(80°) = -sqrt(3)/4.