MATHEMATICS MIDDLE SCHOOL

Let (-6,-5) be a point on the terminal side of theta Find the exact value of sin theta, csc theta, and cot theta

Answers

Answer 1

Answer:

Answer:

Part 1) $sin(\theta)=-(5√(61))/(61)$ or $sin(\theta)=-(5)/(√(61))$

Part 2) $csc(\theta)=-(√(61))/(5)$

Part 3) $cot(\theta)=(6)/(5)$

Step-by-step explanation:

we know that

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

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

$sin(\theta)=(y)/(r)$

we have

$x=6\ units,y=5\ units$

Applying the Pythagoras Theorem

$r^(2)=x^(2)+y^(2)$

substitute

$r^(2)=6^(2)+5^(2)$

$r^(2)=61$

$r=√(61)\ units$ -----> the hypotenuse

substitute

$sin(\theta)=(5)/(√(61))$

Simplify

$sin(\theta)=(5√(61))/(61)$

Remember that the sin(theta) is negative

$sin(\theta)=-(5√(61))/(61)$

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

$csc(\theta)=1/sin(\theta)=(r)/(y)$

we have

$sin(\theta)=-(5)/(√(61))$

$csc(\theta)=-(√(61))/(5)$

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

$cot(\theta)=(x)/(y)$

we have

$x=6\ units,y=5\ units$

substitute

$cot(\theta)=(6)/(5)$

Answer 2

Answer:

Final answer:

The exact values of sin theta, csc theta, and cot theta for a point (-6, -5) on the terminal side are -5/sqrt(61), sqrt(61)/-5, and 6/5 respectively.

Explanation:

In this problem we have a point (-6, -5) on the terminal side of theta. The x-coordinate corresponds to the cosine of theta and the y-coordinate corresponds to the sin theta.

To answer your question:

sin theta = y/r = (-5)/sqrt((-6)^2+(-5)^2) = -5/sqrt(61)
csc theta = 1/sin(theta) = sqrt(61)/-5
cot theta = cos(theta)/sin(theta) = x/y = -6/-5 = 6/5

Learn more about Trigonometric Values here:

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