Select the expression with the same value as the given expression.sin(−38°)\sin\left(-38\degree\right)sin(−38°)

− sin ⁡ 38 ° -\sin38\degree − sin 38°

Select the expression with the same value as the given expression. sin ( − 38 ° ) \sin\left(-38\degree\right) sin ( − 38° )

In this problem, we're asked to select the expression with the same value as the given expression. And the expression that we're given here is sine of negative 38. Now knowing that sine is an odd function tells me that the sine of negative 38 is just going to be equal to negative sine of 38. So that answer is right down here, which tells me that this has the same value as my given expression. Now this first one, the sine of 38 degrees, would only be true if sine was an even function, which it's not. And if I were to simplify this further using my even odd identities, this would actually just end up being equal to sine of 38 degrees, which again is not the correct answer here because sine is not an even function. So the negative sine of 38 degrees has the same exact value of the sine of negative 38 degrees. You can even test this by putting it into your calculator. Thanks for watching and I'll see you in the next one.

Select the expression with the same value as the given expression. sin ⁡ ( − 38 ° ) \sin\left(-38\degree\right) sin ( − 38° )

− sin ⁡ 38 ° -\sin38\degree − sin 38°

sin ⁡ 38 ° \sin38\degree sin 38°

− sin ⁡ ( − 38 ° ) -\sin\left(-38\degree\right) − sin ( − 38° )

1 − sin ⁡ 38 ° \frac{1}{-\sin38\degree} − s i n 38° 1

6. Trigonometric Identities and More Equations

Introduction to Trigonometric Identities

Trigonometry

6. Trigonometric Identities and More Equations

Introduction to Trigonometric Identities

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Multiple Choice

Select the expression with the same value as the given expression.
$\sin\left(-38\degree\right)$

$\sin38\degree$

$-\sin38\degree$

$-\sin\left(-38\degree\right)$

$\frac{1}{-\sin38\degree}$

Verified step by step guidance

Understand the property of the sine function: $ \sin(-x) = -\sin(x) $. This property states that the sine of a negative angle is the negative of the sine of the positive angle.

Apply the property to the given expression $ \sin(-38\degree) $. Using the property, we can rewrite this as $ -\sin(38\degree) $.

Compare the rewritten expression $ -\sin(38\degree) $ with the options provided.

Identify that $ -\sin(38\degree) $ matches one of the options given, which is $ -\sin(38\degree) $.

Conclude that the expression $ \sin(-38\degree) $ is equivalent to $ -\sin(38\degree) $ based on the trigonometric identity.

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