Question

cho sinα=\(\dfrac{-3}{4}\)

Tính A= 5cos²α - 7sin²α

Answer 1

Ta có: \(\sin\alpha=-\dfrac{3}{4}\Rightarrow\alpha\approx-48^\circ35'\)

\(\Rightarrow\cos\alpha\approx0,66\)

\(\Rightarrow\) \(5\cos^2\alpha-7\sin^2\alpha\approx5\left(0,66\right)^2-7\left(-\dfrac{3}{4}\right)^2\approx-1,76\)

Answer 2

\(A=5\left(1-sin^2a\right)-7sin^2a\)

\(=5-12sin^2a\)

\(=5-12\cdot\dfrac{9}{16}=5-9\cdot\dfrac{3}{4}=5-\dfrac{27}{4}=-\dfrac{7}{4}\dfrac{4}{ }\)