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iVinArrow [24]
1 year ago
10

The terminal side of Ø is in quadrant II and cos ø = -5/13 What is sin ø?

Mathematics
1 answer:
Sliva [168]1 year ago
7 0

the value of sin ∅ is 12/ 13

<h3>Quadrants and the "cast" Rule:</h3>
  • In the first quadrant, the values for sin, cos, and tan are positive.
  • In the second quadrant, the values for sin are positive only.
  • In the third quadrant, the values for tan are positive only.
  • In the fourth quadrant, the values for cos are positive only.

From the given question,

We have,  cos ∅= 5/13

From the trigonometric identities, we have that

sin^2\alpha  + cos^2\alpha  = 1

Then , let's substitute the value of cos ∅

sin^2\alpha +(\frac{-5}{13} )^2 = 1

Let make sin the subject of formula and find the squares of the fraction

sin²∅ = 1 - \frac{25}{169}

Find the LCM

sin²∅ = \frac{169 - 25}{169}

Find the difference

sin²∅ = \frac{144}{169}

Find the square root

sin∅ = \sqrt{\frac{144}{159} }

sin∅ = \frac{12}{13}

In quadrant II , sin is positive, so we have

sin ∅ = 12/ 13

Thus, the value of sin ∅ is 12/ 13

Learn more about quadrant  here:

brainly.com/question/863849

#SPJ1

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