Question

If sin 0 = 2/3 what is cos 0? Cos 0 = ✓[?] Simplify your answer if possible.​

Answer 1

To find cos x, we can use the trigonometric identity:

cos^2 x + sin^2 x = 1

Rearranging this identity, we get:

cos^2 x = 1 - sin^2 x

Substituting the given value of sin x (2/3), we get:

cos^2 x = 1 - (2/3)^2

= 1 - 4/9

= 5/9

Taking the square root of both sides, we get:

cos x = ±√(5/9)

Since cosine is positive in the first quadrant, where sin x is positive, we can take the positive square root:

cos x = √(5/9)

We can simplify this expression by noting that both the numerator and denominator have a common factor of 5. We can simplify by factoring out this common factor:

cos x = √(5/9)

= √(5)/√(9)

= √(5)/3

Therefore, cos x = √(5)/3.

Answer 2

To find the value of cos 0 when sin 0 = 2/3, substitute the value of sin 0 into the Pythagorean identity sin^2 0 + cos^2 0 = 1, and solve for cos 0.

Step-by-step explanation:

To find the value of cos 0 when sin 0 = 2/3, we can use the Pythagorean identity. Since sin^2 0 + cos^2 0 = 1, we can substitute the value of sin 0 and solve for cos 0. Here's how:

sin^2 0 + cos^2 0 = 1

(2/3)^2 + cos^2 0 = 1

4/9 + cos^2 0 = 1

cos^2 0 = 1 - 4/9

cos^2 0 = 5/9

cos 0 = ±√(5/9)

Since 0 is in the first quadrant, where cosine is positive, the value of cos 0 is √(5/9), which can be simplified to √5/3.