Find sin x if cos x= 2/3 and x is in quadrant 4

Yes you'll use the half angle identities to solve...it sounds like you understand how to use them just not which sign to use.

This is actually pretty easy. All you have to do is know what quadrant your angle is in and that will determine the sign.

Quadrant1 = all trig functions are positive
Quadrant2 = sine is positive and cosine and tangent are negative
Quadrant3 = tangent is positive and sine and cosine are negative
Quadrant4 = cosine is positive and sine and tangent are negative

since your original angle is in quadrant 4 then the half angle will be in Quadrant 2

so the sine of the half angle is positive and the cosine of the half angle is negative

The sine is negative in quadrant 4

adjacent side = 2 and hypotenuse = 3 so opposite side will be -sqrt 5

so sin x = - sqrt5/ 3

0, 5/7, and -10 are RATIONAL numbers ⇒ 1, 2, 4

Step-by-step explanation:

Rational number are the numbers can be written in the form of the fraction , b ≠ 0

Example:

5, -3, 5.2 , -10.567, , , , , .......5 can be written as -3 can be written as 5.2 can be written as -10.567 can be written as  can be written as can be written as can be written as can be written as

All the numbers above are rational numbers

Let us find the rational numbers in our question

∵ 0 can be written as

∴ 0 is a rational number

∵ is a fraction

∴ is a rational number

∵ 3.6820350285........ can not be written in the form of the fraction

   because we do not know its end (it is an approximated number)

∴ 3.6820350285........ is not a rational number

∵ -10 can be written as

∴ -10 is a rational number

∴ 0, 5/7, and -10 are RATIONAL numbers