Question

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

Answer 1

By using the Pythagorean identity the value of tan $\theta$ will be ∞.

tan $\theta$ = ∞.

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 $\theta$,

$sin \; ^{2} \theta + cos \; ^{2} \theta =1$

By Pythagorean Identity we have,

• $sin \; ^{2} \theta + cos \; ^{2} \theta =1$

we have, $sin \theta \; = \; -1$

So, $(-1)^{2} \; + \; cos^{2}\; \theta =\; 1$

$\; cos^{2}\; \theta =\; 1 - \; 1$

$cos^{2}\; \theta =0$

$cos\; \theta =0$

Now, we know that

$tan \; \theta= \frac{sin\; \theta}{cos\; \theta}$

        =  $\frac{-1}{0}$

  $tan \; \theta=$ ∞....................... (1)

Again, tan $90^{0}$ = ∞

If we compare from equation (1), we have

$\theta = 90^{0}$

Learn more about Pythagorean identity here:

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