Question

find the value of sin150°×cos120°​

Answer 1

Step-by-step explanation:

Can you simplify?

Can you simplify: sin(150°)+cos(120°)?

Short answer: Yes I can

First, sin(150°)=-sin(30°)=-0.5 Correction 0.5

This follows from sin(A-B)=sin(A)cos(B)-sin(B)cos(A); using A=180° and B=30°, we have: sin(150°)=sin(180°)cos(30°)-sin(30°)cos(180°)=-sin(30°) as sin(180°)=0, cos(180°)=-1

Second, cos(120°)=-cos(60°)=-0,5

This follows from cos(A-B)=cos(A)cos(B)+sin(A)sin(B); using A=180° and B=60°, we have: cos(120°)=cos(180°)cos(60°)+sin(180°)sin(60°)=-cos(60°)

Hence sin(150°)+cos(120°)=-0.5–0.5=-1 Correction 0.5–0.5=0