Question

If tany= 0.404,where y is acute, find cos2y.

0.155
16^0
0.719
0.019

Answer 1

Answer on Question #46305 – Math – Trigonometry

1. If $\tan y = 0.404$, where $y$ is acute, find $\cos 2y$.

a. 0.155

b. $16{}^{\circ}$

c. 0.719

d. 0.019

Solution.

We will transform $\cos 2y$ in next way:

$$\cos 2y = \cos^2 y - \sin^2 y = 2 \cos^2 y - 1 = \frac{2}{1 + \tan^2 y} - 1 = \frac{1 - \tan^2 y}{1 + \tan^2 y},$$

where we used $\cos^2 y + \sin^2 y = 1$ and $1 + \tan^2 y = \frac{1}{\cos^2 y}$. Now we can calculate value of $\cos 2y$:

$$\cos 2y = \frac{1 - \tan^2 y}{1 + \tan^2 y} = \frac{1 - (0.404)^2}{1 + (0.404)^2} = \frac{1 - 0.163216}{1 + 0.163216} \approx 0.719.$$

Answer:

0.719.

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