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Alecsey [184]
3 years ago
12

Suppose that theta is an angle in standard position whose terminal side Intersects the unit circle at (-11/61, -60/61)

Mathematics
1 answer:
Blizzard [7]3 years ago
3 0

Answer:

The exact values of the tangent, secant and cosine of angle theta are, respectively:

\cos \theta = -\frac{11}{61}

\tan \theta = \frac{-\frac{60}{61} }{-\frac{11}{61} } = \frac{60}{11}

\sec \theta = \frac{1}{-\frac{11}{61} } = -\frac{61}{11}

Step-by-step explanation:

The components of the unit vector are x = -\frac{11}{61} and y = -\frac{60}{61}. Since r = 1, then x = \cos \theta and y = \sin \theta. By Trigonometry, tangent and secant can be calculated by the following expressions:

\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{y}{x}

\sec \theta = \frac{1}{\cos \theta} = \frac{1}{x}

Now, the exact values of the tangent, secant and cosine of angle theta are, respectively:

\cos \theta = -\frac{11}{61}

\tan \theta = \frac{-\frac{60}{61} }{-\frac{11}{61} } = \frac{60}{11}

\sec \theta = \frac{1}{-\frac{11}{61} } = -\frac{61}{11}

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