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:
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