Find the missing value and round to the nearest hundredth.
1 answer:
You have to use Trigonometric ratios here. I'll help you with a question, and you try to do the other two.
a. You are given the hypotenuse, and told to figure out the opposite. The trigonometric function that deals with that is sin(x), which is opposite over hypotenuse. So:
Solve for y:
Simplify:
For these problems, you have to remember the ratios Sine, Cosine, and Tangent. An easy way is to make a mnemonic device. A good one that a lot of people use is SohCahToa. Which is Sine (Opposite, Hypotenuse), Cosine (Adjacent, Hypotenuse) and Tangent (Opposite, Adjacent). Remember trigonometry is just a glorified field of ratios of sides to angles. There are many more trigonometric ratios including inverse trigonometric ratios, reciprocal trigonometric ratios, and hyperbolic trigonometric ratios (which show up during differential calculus). But for now, focus on this. Haha.
a. You are given the hypotenuse, and told to figure out the opposite. The trigonometric function that deals with that is sin(x), which is opposite over hypotenuse. So:
Solve for y:
Simplify:
For these problems, you have to remember the ratios Sine, Cosine, and Tangent. An easy way is to make a mnemonic device. A good one that a lot of people use is SohCahToa. Which is Sine (Opposite, Hypotenuse), Cosine (Adjacent, Hypotenuse) and Tangent (Opposite, Adjacent). Remember trigonometry is just a glorified field of ratios of sides to angles. There are many more trigonometric ratios including inverse trigonometric ratios, reciprocal trigonometric ratios, and hyperbolic trigonometric ratios (which show up during differential calculus). But for now, focus on this. Haha.
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Answer:
Step-by-step explanation:
I'm guessing you have to simplify the expression so...
first, on the top of the fraction there is a 5^2 which is just 25. 25*25 = 625, so the top of the fraction bar changes to 625 * t^8
The denominator is 10^3 = 1000. this changes it to 1000 * t^4
The hard part now is to simplify this. t^8 is just t*t*t*t*t*t*t*t. similarly t^4 is just t*t*t*t
Since there are 4 t's in both the numerator and denominator, this cancels it out and changes this to
which simplifies to
.
To get rid of the denominator, we multiply 8/8 to the fraction to get:
, which if we distribute the 8 we get:
. Which is our answer!
Hope this helps!