Math

QuestionFind the exact value of the expression using even-odd properties: sin(π2)\sin \left(-\frac{\pi}{2}\right).

Studdy Solution

STEP 1

Assumptions1. We are dealing with the sine function, which is an odd function. . We are aware of the property of odd functions, which states that for any real number x, f(-x) = -f(x).
3. We are familiar with the unit circle and the values of sine at key points on the unit circle.

STEP 2

We can use the property of odd functions to rewrite the expression. For any real number x, f(-x) = -f(x). So, we can writesin(π2)=sin(π2)\sin \left(-\frac{\pi}{2}\right) = -\sin \left(\frac{\pi}{2}\right)

STEP 3

We know that the sine of π2\frac{\pi}{2} is1, from the unit circle. So, we can substitute this value into the equationsin(π2)=1-\sin \left(\frac{\pi}{2}\right) = -1So, the exact value of the expression sin(π2)\sin \left(-\frac{\pi}{2}\right) is -1.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord