Mathematics
ayame
26

Need some help with these last few problems Thank you for your time and help 1. For what x-value(s) does sin(x) = -1? 2. What is the y-value for f(x) = cos(x) when x = -90°? 3. What is the y-value for f(x) = tan(x) when x = -45°? 4. Find the value of e. ( Left Image ) 5. Find the value of b. ( Right Image )

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(1) Answers
jackie1977

(1) On the unit circle, you have [latex]\sin x=-1[/latex] when [latex]x=-\dfrac\pi2[/latex], and more generally this is the case whenever you perform a full rotation about the origin. This means [latex]\sin x=-1[/latex] any time [latex]x=-\dfrac\pi2+2n\pi[/latex] where [latex]n[/latex] is any integer. (2) When [latex]x=-90^\circ[/latex], you have [latex]y=f(-90^\circ)=\cos(-90^\circ)=0[/latex]. (3) When [latex]x=-45^\circ[/latex], you have [latex]y=f(-45^\circ)=\tan(-45^\circ)=-1[/latex]. (4) The law of sines says that [latex]\dfrac{12}{\sin40^\circ}=\dfrac{e}{\sin55^\circ}\implies e\approx15.292[/latex] (5) The law of cosines says that [latex]b^2=6.5^2+8^2-2\times6.5\times8\cos37^\circ\implies b\approx4.816[/latex]

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