已知cos(X-π/4)=√2/10,X∈(π/2 ,3π/4)

问题描述:

已知cos(X-π/4)=√2/10,X∈(π/2 ,3π/4)
(1) 求sinX的值
(2) 求sin (2X+3π)的值

已知cos(X-π/4)=√2/10,X∈(π/2 ,3π/4),所以sin(X-π/4)=(7/10)√2
1 .sinx=sin[(x-π/4)+π/4]=sin(X-π/4)cosπ/4)+cos(X-π/4)sinπ/4)=4/5
所以cosx=-3/5
2 .sin (2X+3π)=-2sinxcosx=-2*4/5*(-3/5)=24/25