Question

can someone check my answer?

Answer 1

If \[\sin \theta=\frac{ 3 }{ 5 }\] and theta terminates in the first quadrant, find the exact value of \[\cos 2\theta\]

Answer 2

In the right-triangle in the diagram, cos(θ) = adjacent side/ hypotenuse = 4/5
Opposite side = sqrt[5^2-4^2] = sqrt[25-16] = sqrt(9) = 3 --- Pyhogorean theorem

Therefore, sin(θ) = 3/5

But sine is negative in quadrant 4 (x-is negative)
Therefore, sin(θ) = -3/5

Answer 3

\[\sin ^{2}\theta+\cos ^{2}\theta=1\]
\[(\frac{ 3 }{ 5 })^{2}+\cos ^{2}\theta=1\]

Answer 4

\[\cos ^{2}\theta=\frac{ 16 }{ 25 }\]
\[\cos \theta=\frac{ 4 }{ 5 }\]

Answer 5

Then, I plugged everything in \[\cos 2\theta=\cos ^{2}\theta-\sin ^{2}\theta\]

Answer 6

\[\cos 2\theta=(\frac{ 4 }{ 5 }) ^{2}-(\frac{ 3 }{ 5 })^{2}\]

Answer 7

What I got was \[\frac{ 7 }{ 25 }\]