Trigonometry Questions

1. Using a compound angle formula, demonstrate that sin2π/3 is equivalent to sin π/3

2. The expression sinπ is equal to zero, while the expression 1/cscπ is undefined. Why is the identity sin(theta)=1/csc(theta) still an identity?

3. Why do the solutions to the equation cos^2x = 3/4 lie in all four quadrants?

1 answer

sin(2π/3) = sin(π-π/3) = sinπ cosπ/3 - cosπ sinπ/3 = 0+sinπ/3

1/0 is undefined.

cosx = ±√3/2
cosx > 0 in QI,QIV
cosx < 0 in QII,QIII