Lilmay2112idn
Answered

IDNLearn.com: Your destination for reliable and timely answers to any question. Discover the reliable solutions you need with help from our comprehensive and accurate Q&A platform.

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

Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Thank you for choosing IDNLearn.com for your queries. We’re here to provide accurate answers, so visit us again soon.