If \sin\theta-\cos\theta=\frac{1}{5}, what is \sin\theta\cos\theta?

\frac{12}{25} (\sin\theta-\cos\theta)^2=1-2\sin\theta\cos\theta=\frac{1}{25}, so 2\sin\theta\cos\theta=\frac{24}{25} and \sin\theta\cos\theta=\frac{12}{25}.

Right Triangles and Trigonometry

SAT Math· difficulty 4/5

\sin\theta-\cos\theta=\frac{1}{5}

A
$\frac{24}{25}$
B
$\frac{13}{25}$
C
$\frac{1}{25}$
D
$\frac{12}{25}$
check_circle

Explanation

(\sin\theta-\cos\theta)^2=1-2\sin\theta\cos\theta=\frac{1}{25}

Want 10 more like this — adaptive to your weak spots?

Practice 10 like thisarrow_forward Predict my AP score

Related questions