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2 years ago

Find the exact value of sec theta if csc theta = -4/3 and the terminal side of theta lies in quadrant III

Mathematics

1 answer:

GREYUIT [131]2 years ago

3 0

Answer:

-4 sqrt(7)/7

Step-by-step explanation:

csc theta = -4/3

csc theta = hypotenuse / opposite side

hypotenuse = 4

opposite = 3

Using the pythagorean theorem

a^2 + b^2 = c^2

3^2 + b^2 = 4^2

9+b^2 = 16

b^2 = 16-9

b^2 = 7

Taking the square root

sqrt(b^2) = sqrt(7)

b = sqrt(7)

We are in the third quadrant so only tan and cot are positive

that means the x and y values are "negative" so a = -3 and b = - sqrt(7)

sec theta = hypotenuse / adjacent

= 4/ - sqrt(7)

rationalizing

-4 sqrt(7)/ sqrt(7)* sqrt(7)

= -4 sqrt(7)/7

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