lilmay2112
Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Use the Pythagorean Identity and Tangent Identity to find tan theta if sin theta= -1 and 0 ≤ theta <2Pi radians.

Sagot :

By using the Pythagorean identity the value of tan [tex]\theta[/tex] will be ∞.

tan [tex]\theta[/tex] = ∞.

What is Pythagorean identity?

Pythagorean identities are identities in trigonometry that are extensions of the Pythagorean theorem. The fundamental identity states that for any angle [tex]\theta[/tex],

[tex]sin \; ^{2} \theta + cos \; ^{2} \theta =1[/tex]

By Pythagorean Identity we have,

  • [tex]sin \; ^{2} \theta + cos \; ^{2} \theta =1[/tex]

we have, [tex]sin \theta \; = \; -1[/tex]

So, [tex](-1)^{2} \; + \; cos^{2}\; \theta =\; 1[/tex]

[tex]\; cos^{2}\; \theta =\; 1 - \; 1[/tex]

[tex]cos^{2}\; \theta =0[/tex]

[tex]cos\; \theta =0[/tex]

Now, we know that

[tex]tan \; \theta= \frac{sin\; \theta}{cos\; \theta}[/tex]

        =  [tex]\frac{-1}{0}[/tex]

  [tex]tan \; \theta=[/tex] ∞....................... (1)

Again, tan [tex]90^{0}[/tex] = ∞

If we compare from equation (1), we have

[tex]\theta = 90^{0}[/tex]

Learn more about Pythagorean identity here:

https://brainly.com/question/10285501

#SPJ1

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.