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Allushta [10]
3 years ago
11

Let (-6,-5) be a point on the terminal side of theta

Mathematics
1 answer:
Georgia [21]3 years ago
5 0

Answer:

Part 1) sin(\theta)=-\frac{5\sqrt{61}}{61}  or sin(\theta)=-\frac{5}{\sqrt{61}}

Part 2) csc(\theta)=-\frac{\sqrt{61}}{5}

Part 3) cot(\theta)=\frac{6}{5}

Step-by-step explanation:

we know that

The point (-6,-5) lies on the III Quadrant

so

sin(theta) is negative

csc(theta) is negative

cot(theta) is positive

Part 1) Find the sine of angle theta

we know that

The function sine is equal to divide the opposite side to the angle theta by the hypotenuse

sin(\theta)=\frac{y}{r}

we have

x=6\ units,y=5\ units

Applying the Pythagoras Theorem

r^{2}=x^{2}+y^{2}

substitute

r^{2}=6^{2}+5^{2}

r^{2}=61

r=\sqrt{61}\ units -----> the hypotenuse

substitute

sin(\theta)=\frac{5}{\sqrt{61}}

Simplify

sin(\theta)=\frac{5\sqrt{61}}{61}

Remember that the sin(theta) is negative

so

sin(\theta)=-\frac{5\sqrt{61}}{61}

Part 2) Find the cosecant of angle theta

we know that

The function cosecant is equal to divide the hypotenuse by the opposite  side to the angle theta

csc(\theta)=1/sin(\theta)=\frac{r}{y}

we have

sin(\theta)=-\frac{5}{\sqrt{61}}

so

csc(\theta)=-\frac{\sqrt{61}}{5}

Part 3) Find the cotangent of angle theta

we know that

The function cotangent is equal to divide the adjacent side to the angle theta by the opposite side to the angle theta

cot(\theta)=\frac{x}{y}

we have

x=6\ units,y=5\ units

substitute

cot(\theta)=\frac{6}{5}

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The correct format of the question is

At the end of 2006, the population of Riverside was 400 people. The population for this small town can be modeled by the equation below, where t represents the number of years since the end of 2006 and P represents the number of people. P = 400 ( 1.2 )^ t Based on this model, approximately what was the increase in the population of Riverside at the end of 2009 compared to the end of 2006?

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Step-by-step explanation:

We are given the equation as P = 400 ( 1.2 )^ t

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