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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

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