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[MVP123]

For en vinkel a i andre kvadrant har vi cos a = - 4/5

Finn eksakte verdier for
a) sin2a
b) tan2a

JEg får ikke til disse to oppgavene

[Olorin]

skriv om sin2a
[tex]\cos a=-\frac45[/tex]
[tex]a=\arccos(-\frac45)[/tex]

[tex]\sin(2a)=2\sin a\cos a[/tex]

[tex]\sin a=\sqr{1-\cos^2a}=\sqr{1-(-\frac45)^2}=\sqr{\frac9{25}}=\frac35[/tex]

Setter inn:

[tex]\sin(2a)=2\sin a \cdot \cos a=2\cdot \frac35\cdot (-\frac45)=-\frac{24}{25}[/tex]

[Olorin]

[tex]\tan(2a)=\frac{2\tan a}{1-\tan^2a}[/tex]

[tex]a=\arccos(-\frac45)=\arctan(\frac{\sqr{5^2-(-4)^2}}{-4})=\arctan(-\frac34)[/tex]

[tex]\tan a = \tan(\arctan(-\frac34)=-\frac34[/tex]

[tex]\tan(2a)=\frac{2\cdot(-\frac34)}{1-(-\frac34)^2}=\frac{-\frac32}{\frac7{16}}=-\frac{24}{7}[/tex]

[MVP123]

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