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Katena32 [7]
3 years ago
15

What is the value of cos(x) if tan ( x)= -2 and x is in quadrant of IV?

Mathematics
1 answer:
scoray [572]3 years ago
4 0

Answer:

cos(x)=\frac{\sqrt{5}}{5}

Step-by-step explanation:

we have that

tan(x)=-2

The angle x is in quadrant IV

That means ---> The value of cos(x) is positive and the value of sin(x) is negative

Remember that

cos^2(x)+sin^2(x)=1 ----> equation A

tan(x)=\frac{sin(x)}{cos(x)}

so

-2=\frac{sin(x)}{cos(x)}

sin(x)=-2cos(x) ----> equation B

substitute equation B in equation A

cos^2(x)+(-2cos(x))^2=1

solve for cos(x)

cos^2(x)+4cos^2(x)=1

5cos^2(x)=1

cos^2(x)=\frac{1}{5}

square root both sides

cos(x)=\pm\frac{1}{\sqrt{5}}

but remember that the value of cos(x) is positive (IV quadrant)

cos(x)=\frac{1}{\sqrt{5}}

simplify

cos(x)=\frac{\sqrt{5}}{5}

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