Which of the following words does not indicate multiplication?

Find exact values for sin θ, cos θ and tan θ if sec θ = 6/5 and tan θ < 0

k0ka [10]

$\bf sin(\theta)=\cfrac{opposite}{hypotenuse}
\qquad \qquad 
% cosine
cos(\theta)=\cfrac{adjacent}{hypotenuse}
\\ \quad \\
% tangent
tan(\theta)=\cfrac{opposite}{adjacent}
\qquad \qquad 
% secant
sec(\theta)=\cfrac{hypotenuse}{adjacent}\\\\
-----------------------------\\\\
sec(\theta)=\cfrac{6}{5}\cfrac{\leftarrow hypotenuse}{\leftarrow adjacent}
\\\\\\
$

$\bf \textit{so.. using the pythagorean theorem, we get}
\\\\\\
c^2=a^2+b^2\implies \pm \sqrt{c^2-a^2}=b\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite
\end{cases}
\\\\\\
\textit{that simply means that }\pm \sqrt{6^2-5^2}=b\implies \pm \sqrt{11}=b$

but.. which is it, the positive or negative version of "b"? well.... we know tangent is < 0, that's another way of saying, tangent is negative

now.. .tangent is opposite over adjacent... for tangent to be negative, the sign of those two must differ

so.. where does that happens? well, it happens on the 2nd and 4th quadrants, so..... which quadrant then?

well, we know the hypotenuse is always positive, is just the radius anyway, and in this case is 6
but the adjacent is positive 5, that means the adjacent is positive, thus the opposite must be negative, and that happens on the 4th quadrant

so that means $\bf -\sqrt{11}=b$

so... now, you have all three sides, the hypotenuse, the adjacent, and the opposite, so, just fill those in, in the ratios for cosine, sine and tangent

6 0

3 years ago

74.94×103=

STatiana [176]

7494 thousand is the answer

3 0

3 years ago

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A man with a height of 5ft casts a shadow of 2ft. What will be the height of a tree that casts a shadow of 40ft at the same time

Juliette [100K]

Answer:

19

Step-by-step explanation:

4 0

3 years ago

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jocelyn bought 2 sweaters for the same price.she paid $23.56, including sales tax of $1.36 and a $5.00 discount coupon.what was

k0ka [10]

Jocelyn bought 2 sweaters for the same price.
She paid $23.56, including sales tax of $1.36 and a $5.00 discount coupon.
Problem: Find the price of 1 sweater before the tax and coupon
=> 2 sweaters = 23.56 dollars included tax and discount
=> remove the tax and discount first
=> 23.56 + 5.00 = 28.56 dollars since this is a discount, we need to add this to the amount
=> 28.56 – 1.36 = 27.2 dollars is the price of 2 sweaters
=> 1 sweater costs 13.6 dollars

4 0

2 years ago

Ayo runs a fairground game.In each turn, a player rolls a fair dice numbered 1 - 6 and spins a fair spinner numbered 1 - 12.It c

aksik [14]

Using the definition of expected value, it is found that Ayo can be expected to make a profit of £55.8.

The expected value is given by the sum of each outcome multiplied by it's respective probability.

In this problem:

The player wins $6, that is, Ayo loses £6, if he rolls a 6 and spins a 1, hence the probability is $\frac{1}{6} \times \frac{1}{12} = \frac{1}{72}$ .

The player wins $3, that is, Ayo loses £3, if he rolls a 3 on at least one of the spinner or the dice, hence, considering three cases(both and either the spinner of the dice), the probability is $\frac{1}{6} \times \frac{1}{12} + \frac{1}{6} \times \frac{11}{12} + \frac{5}{6} \times \frac{1}{12} = \frac{1 + 11 + 5}{72} = \frac{17}{72}$

In the other cases, Ayo wins £1.40, with $1 - \frac{18}{72} = \frac{54}{72}$ probability.

Hence, his expected profit for a single game is:

$E(X) = -6\frac{1}{72} - 3\frac{17}{72} + 1.4\frac{54}{72} = \frac{-6 - 3(17) + 54(1.4)}{72} = 0.2583$

For 216 games, the expected value is:

$E = 216(0.2583) = 55.8$

Ayo can be expected to make a profit of £55.8.

To learn more about expected value, you can take a look at brainly.com/question/24855677

6 0

2 years ago