Question

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

Answer 1

the value of sin ∅ is 12/ 13

Quadrants and the "cast" Rule:

• 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:

https://brainly.com/question/863849

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