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3 years ago

How to tell when to use sin, cos or tan

Mathematics

1 answer:

lions [1.4K]3 years ago

3 0

Answer:

Step-by-step explanation:

Keep in mind that these three trig functions can be interpreted as being the ratios of the side lengths of a triangle:

opposite side

sin x = ----------------------

hypotenuse

adjacent side

cos x = ----------------------

hypotenuse

opposite side

tan x = ----------------------

adjacent side

In the case where you have a right triangle and know the lengths of two of its three sides, that knowledge dictates which of the above trig functions to use in "solving the triangle."

------------------------------------------------------------------------------------------------------------

If, for example, the "opposite side" of a triangle is 3 and the "hypotenuse" is 5, we'd choose to use the sine function to find the angle opposite the "opposite side:"

opposite side 3 units

sin x = ---------------------- = -------------

hypotenuse 5 units

Find x by using the inverse sine function:

Angle x = arcsin 3/5 = 0.644 radians or 36.9 degrees.

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4 years ago

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3 years ago

Suppose you pay a dollar to roll two dice. if you roll 5 or a 6 you Get your dollar back +2 more just like it the goal will be t

LiRa [457]

Answer:

(a)$67

(b)You are expected to win 56 Times

(c)You are expected to lose 44 Times

Step-by-step explanation:

The sample space for the event of rolling two dice is presented below

$(1,1), (2,1), (3,1), (4,1), (5,1), (6,1)\\(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)\\(1,3), (2,3), (3,3), (4,3), (5,3), (6,3)\\(1,4), (2,4), (3,4), (4,4), (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)$

Total number of outcomes =36

The event of rolling a 5 or a 6 are:

$(5,1), (6,1)\\ (5,2), (6,2)\\( (5,3), (6,3)\\ (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)$

Number of outcomes =20

Therefore:

P(rolling a 5 or a 6) $=\dfrac{20}{36}$

The probability distribution of this event is given as follows.

$\left|\begin{array}{c|c|c}$Amount Won(x)&-\$1&\$2\\&\\P(x)&\dfrac{16}{36}&\dfrac{20}{36}\end{array}\right|$

First, we determine the expected Value of this event.

Expected Value

$=(-\$1\times \frac{16}{36})+ (\$2\times \frac{20}{36})\\=\$0.67$

Therefore, if the game is played 100 times,

Expected Profit =$0.67 X 100 =$67

If you play the game 100 times, you can expect to win $67.

(b)

Probability of Winning $=\dfrac{20}{36}$

If the game is played 100 times

Number of times expected to win

$=\dfrac{20}{36} \times 100\\=56$ times$

Therefore, number of times expected to loose

= 100-56

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4 years ago

Skyler buys 8 T-Shirts and 5 hats for $220. The next day, he buys 5 T-shirts and 1 hat for $112. i need the equation

tester [92]

Answer:

13t + 6h = $332

Step-by-step explanation:

The variable for shirts is t. The variable for hats is h.

8 shirts plus 5 shirts is 13 shirts. (13t)

5 hats plus 1 hat is 6 hats. (6h)

$220 plus $112 is $332. The total cost will be $332.

13t + 6h = $332

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4 years ago

jok3333 [9.3K]

A. X^4. Hope this helped!

8 0

3 years ago

How to tell when to use sin, cos or tan​

How to tell when to use sin, cos or tan