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

12. Trigonometric Identities

Introduction to Trigonometric Identities

Precalculus

12. Trigonometric Identities

Introduction to Trigonometric Identities

Struggling with Precalculus?

Join thousands of students who trust us to help them ace their exams!Watch the first video

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 this property to the given expression $ \sin(-38\degree) $. According to the property, $ \sin(-38\degree) = -\sin(38\degree) $.

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

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

Conclude that the correct expression with the same value as $ \sin(-38\degree) $ is $ -\sin(38\degree) $.

6:19m

Watch next

Master Even and Odd Identities with a bite sized video explanation from Patrick

Start learning

Introduction to Trigonometric Identities practice set

Problem sets built by lead tutors

Expert video explanations

Go to Practice