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Matthew S.
Graduated with B.S. Mathematics at Indiana University East
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Pre-Calculus
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Question:

Find $$tan\theta$$ if $$sin \theta=\frac{24}{25}$$ and $$\theta$$ is in Quadrant II.

Matthew S.

We know that $$tan\theta=\frac{sin\theta}{\cos\theta}$$. Therefore, to find $$tan\theta$$, we must first find $$cos\theta$$. We can do this by using the trig identity $$cos^2 \theta=1-sin^2 \theta$$. $(cos^2 \theta=1-sin^2 \theta$). We know that $$sin\theta=\frac{24}{25}$$, therefore: $(cos^2 \theta=1-sin^2 \theta$) $(cos^2 \theta=1-(\frac{24}{25})^2$) $(cos^2 \theta=1-\frac{576}{625}$) $(cos^2 \theta=\frac{49}{625}$) $(cos\theta=\pm \frac{7}{25}$) Now, since $$\theta$$ is in Quadrant II, we know that $$cos\theta< 0$$. Therefore, we know that $$cos\theta=- \frac{7}{25}$$. Now we can solve for $$tan\theta$$. $(tan\theta= \frac{sin\theta}{cos\theta}$) $(tan\theta= \frac{\frac{24}{25}}{\frac{-7}{25}}$) $(tan\theta= -\frac{24}{7}$)

Pre-Algebra
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Question:

Solve the equation: $(5x-3x=-20$)

Matthew S.

To solve this equation, we first simplify our variables, in this case, $$x$$. To simplify $$5x-3x$$, we subtract our coefficients, $$5-3$$, which is $$2$$, therefore $$5x-3x$$ is $$2x$$. So far we have: $(5x-3x=-20$) $(2x=-20$) Now to solve for $$x$$, we must divide $$-20$$ by $$2$$. $(2x=-20$) $(x=-10$) Therefore, the solution of the equation is $$x=-10$$

Algebra
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Question:

Solve the following system of equations by substitution: $$y=5x-1$$, $$2y=3x+12$$

Matthew S.

Our first step to solve is to plug $$y=5x-1$$ into the equation $$2y=3x+12$$. $(2y=3x+12$) $(2(5x-1)=3x+12$) Now we can solve for $$x$$: $(2(5x-1)=3x+12$) $(10x-2=3x+12$) Now we subtract $$3x$$ from both sides and add $$2$$ to both sides, giving us our like terms and the same side of the equals sign: $(7x=14$) $(x=2$) Now we can plug $$x=2$$ back into the equation $$y=5x-1$$ $(y=5x-1$) $(y=5(2)-1$) $(y=9$) This gives us our solution: $((2,9)$) Now we can double check our answers by plugging them back into the original equations. $(y=5x-1$) $(9=5(2)-1$) $(9=9$) And $(2y=3x+12$) $(2(9)=3(2)+12$) $(18=18$) Since both of our equations agree, we have found that $$(2,9)$$ is a solution to the given system of equations.

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