Use the triangle to answer the question.

Mathematics

1 answer:

Oksana_A [137]4 years ago

7 0

Answer: Choice D) sin(x)/cos(y) = 1

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Label the sides as shown in the image attachment.

P = horizontal leg (opposite of angle x; adajcent to angle y)
Q = vertical leg (opposite of angle y; adajcent to angle x)
R = hypotenuse (longest side; always opposite the 90 degree angle)

Use the definitions of sine and cosine to say...

sin(Angle) = opposite/hypotenuse
sin(x) = P/R

and

cos(angle) = adjacent/hypotenuse
cos(y) = P/R

Notice how sin(x) = cos(y). This is true any time x+y = 90 which is the case here (x and y are complementary angles). A more specific example is sin(30) = cos(60) which are both equal to 1/2 or 0.5

Since sin(x) = cos(y), this means sin(x)/cos(y) = 1 as any expression divided by itself is equal to 1. Keep in mind that cos(y) cannot equal zero.

This is why choice D is the final answer.

side note: something like cos(x)/sin(y) or sin(y)/cos(x) or similar are all equal to 1 as long as x+y = 90

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(Algebra II ) What is the equation of y = x^3 with the given transformations? vertical compression by a factor of 1/7, horizonta

NNADVOKAT [17]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\

\begin{array}{rllll}
% left side templates
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\mathbb{R}^{{{ B}}x+{{ C}}}+{{ D}}
\end{array}$ $\bf \begin{array}{llll}
% right side info
\bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\
\bullet \textit{ vertical shift by }{{ D}}\\
\qquad if\ {{ D}}\textit{ is negative, downwards}\\
\qquad if\ {{ D}}\textit{ is positive, upwards}
\end{array}$

$\bf ----------------------------\\
f(x)=x^3\textit{compression by }\frac{1}{7}\quad or\quad A=7
\\ \quad \\
f(x)=7x^3\impliedby \textit{8 units to the left, or }C=+8
\\ \quad \\
f(x)=7(x+8)^3\impliedby \textit{now, reflection over x-axis, means}
\\ \quad \\
f(x)=-7(x+8)^3\impliedby \textit{a negative leading term's coefficient}$

6 0

3 years ago

The first two steps in the derivation of the quadratic formula by completing the square are shown below. Which answer choice sho

Dmitriy789 [7]

You didn’t provide any answer choices but you can use my notes to guide you. Hope this helps! :)