Question

If A is acute and cos2A = -7/9 find without a calculator: a) cosA b) sinA

Answer 1

Use
a) Cos2A= [2Cos^2(A)-1]=(-7/9)
b) SinA=Sqrt(1-cos^2(A))

Answer 2

Because A is acute, it is between 0 and 90 degrees. You can use the half angle formula, but in this case it is not really needed. You just need to see where cos2A = -7/9, then take half of that. Should be two possible answers and only one of them will be acute. Then develop your solutions from there.

Answer 3

\[\cos 2A=2\cos ^{2}A-1=-\frac{ 7 }{9 }\]
\[2\cos ^{2}A=\frac{ -7 }{ 9 }+1=\frac{ 2 }{ 9 }\]
\[\cos ^{2}A=\frac{ 1 }{ 9 }\]
\[\cos A=\frac{ 1 }{ 3 } ...\left( A is accute \right)\]
Again \[\cos 2A=1-2\sin ^{2}A\]
You can find sin A