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3 years ago

If sin theta = 4/5 and theta is in quadrant 2, the value of cot theta is

Mathematics

2 answers:

trasher [3.6K]3 years ago

8 0

Answer:

Cot(theta) = - 0.75 or -3/4

Step-by-step explanation:

The hypotenuse is 5

The y value is 4

We need to find the corresponding x value.

x^2 + y^2 = z^2

X = ?

y = 4

z = 5

x^2 + 4^2 = 5^2

x^2 + 16 = 25

x^2 = 9

Now in this case, you are in quadrant 2, so the x value is - 3

sqrt(x^2) = sqrt(9)

x = - 3

The cot value is the adjacent (x value) / the opposite ( y ) value

Cot(theta) = -3/4

cot(theta) = -0.75

xenn [34]3 years ago

4 0

Answer:

cotθ = -3/4

Step-by-step explanation:

Given:

sinθ = 4/5

θ is in Quadrant II, so cosθ < 0

Recall:

cotθ = cosθ/sinθ

cos²θ + sin²θ = 1

Determine cosθ:

cosθ = -√(1-sin²θ) = -√(1-(4/5)²) = -√(1-16/25) = -√(9/25) = -3/5

Determine cotθ:

cotθ = cosθ/sinθ = (-3/5)/(4/5) = (-3/5)(5/4) = -15/20 = -3/4

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3 years ago

Write the equation of a line that passes through the point (1,4) and has a slope of 9.

Kryger [21]

Answer:

y=9x-5

Step-by-step explanation:

You want to find the equation for a line that passes through the point (1,4) and has a slope of 9.

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

To start, you know what m is; it's just the slope, which you said was 9. So you can right away fill in the equation for a line somewhat to read:

y=9x+b.

Now, what about b, the y-intercept?

To find b, think about what your (x,y) point means:

(1,4). When x of the line is 1, y of the line must be 4.

Because you said the line passes through this point, right?

Now, look at our line's equation so far: b is what we want, the 9 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specifically passes through the point (1,4).

So, why not plug in for x the number 1 and y the number 4? This will allow us to solve for b for the particular line that passes through the point you gave!.

(1,4). y=mx+b or 4=9 × 1+b, or solving for b: b=4-(9)(1). b=-5.The equation of the line that passes through the point (1,4) with a slope of 9

y=9x-5

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3 years ago