Correct option is D) -0.6.
Step-by-step explanation:
We have [tex]sin\alpha = -0.8[/tex] . Also, we know that [tex]cos\alpha = \sqrt{1- (sin\alpha } )^{2}[/tex] . Let's find out value of [tex]cos\alpha[/tex] using above formula:
[tex]cos\alpha = \sqrt{1- (sin\alpha } )^{2}[/tex]
⇒ [tex]cos\alpha = \sqrt{1- (sin\alpha } )^{2}[/tex]
⇒ [tex]cos\alpha = \sqrt{1- (-0.8 } )^{2}[/tex]
⇒ [tex]cos\alpha = \sqrt{1- (0.64 } )^{}[/tex]
⇒ [tex]cos\alpha = \sqrt{0.36}[/tex]
⇒ [tex]cos\alpha = 0.6[/tex]
But we know that cos[tex]\alpha[/tex] is negative in third quadrant , Therefore [tex]cos\alpha = -0.6[/tex].
Hence, correct option is D) -0.6.
