Question

If sin = O =5/6, what are the values of cos O and tan O? (2 points)​

Answer 1

Answer:

$cos(\alpha )=\frac{\sqrt{11} }{6}$ and $tan(\alpha )=\frac{5\sqrt{11} }{11}$

Step-by-step explanation:

First we would need to solve for the missing leg in order to figure out the remaining answers.

To do this we can use the Pythagorean Theorem a² + b² = c²

Our missing leg in this case is a, so solving for a gives us $a=\sqrt{c^{2} -b^{2} }$

Here our b is 5 and our c is 6. So plugging in these values we get $a=\sqrt{(6)^{2}-(5)^{2} } =\sqrt{36-25} =\sqrt{11}$

With this missing leg being solved, we can use trig identities to solve for cos and tan

I used the trig identity $sin(\alpha )=\frac{opposite}{hypotenuse}$ to set up the triangle in the attached image. We can use the trig identity $cos(\alpha)=\frac{adjacent}{hypotenuse}$ which would give us $cos(\alpha )=\frac{\sqrt{11} }{6}$ and we can use the trig identity $tan(\alpha ) = \frac{opposite}{adjacent}$ which would give us $tan(\alpha )=\frac{5}{\sqrt{11} } =\frac{5\sqrt{11} }{11}$

Answer 2

Answer:

As trigonometry property:

(sinO)^2 + (cosO)^2 = 1

tanO = sinO/cosO

Then, if sinO = 5/6  = 0.83

=> (5/6)^2 + (cosO)^2 = 1

=> cosO = +/- sqrt(1 - (5/6)^2) = +/- 0.55

=>tanO = +/- 0.83/0.55 = +/- 1.51

Hope this helps!

:)