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3 years ago

6

The point (1, −1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of

θ? Make sure to show all work.

1 answer:

mixer [17]3 years ago

6 0

Notice the picture below

x = 1 and y = -1

now... recall your SOH CAH TOA $\bf sin(\theta)=\cfrac{y}{r}
\qquad 
% cosine
cos(\theta)=\cfrac{x}{r}
\qquad 
% tangent
tan(\theta)=\cfrac{y}{x}$

now.. what's the value for "r" or the radius? well, using the pythagorean theorem $\bf c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}\qquad 
\begin{cases}
a=x\\
b=y\\
c=r
\end{cases}$

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7. All of the following are perfect square trinomials EXCEPT one. Which is it?

wolverine [178]

Answer:

All answers EXCEPT answer C. are perfect square trinomials.

Step-by-step explanation:

A perfect square trinomial is polynomial that satisfies the following condition:

$(a+b)^{2} = a^{2}+2\cdot a \cdot b + b^{2}$ , $\forall\,a,b\in\mathbb{R}$

Let prove if each option observe this:

a) $4\cdot x^{2} + 12\cdot x\cdot y + 9\cdot y^{2}$

1) $4\cdot x^{2} + 12\cdot x\cdot y + 9\cdot y^{2}$ Given

2) $(2\cdot x)^{2}+ 2\cdot (2\cdot x)\cdot (3\cdot y)+(3\cdot y)^{2}$ Definition of power/Distributive, associative and commutative properties.

3) $a = 2\cdot x$ , $b = 3\cdot y$ Definition of perfect square trinomial/Result.

b) $9\cdot a^{2}-36\cdot a + 36$

1) $9\cdot a^{2}-36\cdot a + 36$ Given.

2) $(3\cdot a)^{2}-2\cdot (3\cdot a)\cdot 6 + 6^{2}$ Definition of power/Distributive, associative and commutative properties.

3) $a = 3\cdot a$ , $b = 6$ Definition of perfect square trinomial/Result.

c) $x\cdot y^{2}-4\cdot x^{2}\cdot y^{2}+4\cdot x^{2}\cdot y^{2}$

1) $x\cdot y^{2}-4\cdot x^{2}\cdot y^{2}+4\cdot x^{2}\cdot y^{2}$ Given

2) $x\cdot y\cdot (1-4\cdot x+4\cdot x)$ Distributive property.

3) $x\cdot y \cdot 1$ Existence of the additive inverse/Modulative property.

4) $x\cdot y$ Modulative property/Result.

d) $a^{2}\cdot b^{2}+4\cdot a^{3}\cdot b + 4\cdot a^{4}$

1) $a^{2}\cdot b^{2}+4\cdot a^{3}\cdot b + 4\cdot a^{4}$ Given

2) $(a\cdot b)^{2}+2\cdot (a\cdot b)\cdot (2\cdot a^{2})+(2\cdot a^{2})$ Definition of power/Distributive, associative and commutative properties.

3) $a = a\cdot b$ , $b = 2\cdot a^{2}$ Definition of perfect square trinomial.

All answers EXCEPT answer C. are perfect square trinomials.

8 0

3 years ago

Mr and Mrs Kosley took their dog on a walk. Mr Kosley walks 5mph and Mrs Kosley walks 6mph. The dog walks 10mph. On the path, th

Nuetrik [128]

Answer:

ok boomer

Step-by-step explanation:

3 0

2 years ago

Solve the equation (3x-5)=16<br>with working<br>=

Delvig [45]

Answer:

x=7

Step-by-step explanation:You can plug in the value for x and solve to see if true.

7 0

3 years ago

Dange measures and finds that she can do a vertical jump of 27.5% of her height. If Dange is 48 inches tall, how high can she ju

sveta [45]

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{27.5\% of 48}}{\left( \cfrac{27.5}{100} \right)48}\implies 13.2$

5 0

3 years ago

Bob ate 10 carrots and 7 hershey's kisses and the total calories were 263. fred ate 4 carrots and 8 hershey's kisses and the tot

Zarrin [17]

Two equations

let c the calories in carrot
let h the <span>calories in </span><span>hershey's kisses
</span><span>

4c + 8h = 230 eq 1</span>
10 c + 7 h = 263 eq 2

to solve the solution we multiply eq 1 by 10
we multiply <span>eq 2 by 4
</span>
40 c + 80 h = 2300
40c + 28 h = 1052

we subtract the two equations we get
52 h = 1248

h= 24

and so in replacing h = 24 in the equation we get c = 9.5

4 0

3 years ago