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almond37 [142]
2 years ago
13

The angle \theta_1θ

Mathematics
1 answer:
enyata [817]2 years ago
8 0

Answer:

sin\theta_1 = \dfrac{\sqrt{217}}{19}

Step-by-step explanation:

It is given that:

cos\theta_1 = -\dfrac{12}{19}

And we have to find the value of sin\theta_1 = ?

As per trigonometric identities, the relation between sin\theta\ and \ cos\theta can represented as:

sin^2\theta + cos^2\theta = 1

Putting \theta_1 in place of \theta Because we are given

sin^2\theta_1 + cos^2\theta_1 = 1

Putting value of cosine:

cos\theta_1 = -\dfrac{12}{19}

sin^2\theta_1 + (\dfrac{12}{19})^2 = 1\\\Rightarrow sin^2\theta_1 + \dfrac{144}{361} = 1\\\Rightarrow sin^2\theta_1 = 1-\dfrac{144}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{361-144}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{217}{361}\\\Rightarrow sin\theta_1 = +\sqrt{\dfrac{217}{361}}, -\sqrt{\dfrac{217}{361}}\\\Rightarrow sin\theta_1 = +\dfrac{\sqrt{217}}{19}, -\dfrac{\sqrt{217}}{19}

It is given that \theta_1 is in 2nd quadrant and value of sine is always positive in 2nd quadrant. So, the answer is.

\Rightarrow sin\theta_1 = \dfrac{\sqrt{217}}{19}

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