Question

In which quadrant does θ lie if the following statements are true: sin > θ
0 and cos θ >
⁡

Answer 1

Since sin > θ is positive in the first and second quadrants and cos θ > 0 is positive in the first and fourth quadrants, θ could lie in either the first or fourth quadrant.

Answer 2

In which quadrant does θ lie if the following statements are true: sin > θ
0 and tan θ >

Answer 3

Since sin > θ is positive in the first and second quadrants and tan θ > 0 is positive in the first and third quadrants, θ must lie in the first quadrant.

Answer 4

In which quadrant does θ lie if the following statements are true: tan < θ
0 and sin θ < 0

Answer 5

Since tan < θ is negative in the second and fourth quadrants and sin θ < 0 is negative in the third and fourth quadrants, θ must lie in the fourth quadrant.

Answer 6

Find the exact value of tan N in simplest form.
one side = √31
another √47
another 4

Answer 7

We can use the tangent formula to find the value of tan N:

tan N = opposite/adjacent

In this case, the opposite side is √47 and the adjacent side is 4. To find the value of the hypotenuse, we can use the Pythagorean theorem:

h^2 = (√31)^2 + (√47)^2 + 4^2
h^2 = 31 + 47 + 16
h^2 = 94 + 16
h^2 = 110
h = √110

Now we can plug in the values for the opposite, adjacent, and hypotenuse sides:

tan N = √47/4

To simplify, we can rationalize the denominator by multiplying both the numerator and denominator by √4:

tan N = (√47/4) x (√4/√4)
tan N = √188/4
tan N = √47/2

Therefore, the exact value of tan N in simplest form is √47/2.

Answer 8

Find the exact value of cot H in simplest form.
hypotenuse = √31
opposite to ∠N = √15
adjacent to ∠N = 4

Answer 9

We can use the definition of cotangent to find the value of cot H:

cot H = adjacent/opposite

In this case, the adjacent side is 4 and the opposite side is √15. To find the value of the hypotenuse, we can use the Pythagorean theorem:

h^2 = (√31)^2 + (√15)^2
h^2 = 31 + 15
h^2 = 46
h = √46

Now we can plug in the values for the adjacent, opposite, and hypotenuse sides:

cot H = 4/√15

To simplify, we can rationalize the denominator by multiplying both the numerator and denominator by √15:

cot H = (4/√15) x (√15/√15)
cot H = 4√15/15

Therefore, the exact value of cot H in simplest form is 4√15/15.

Answer 10

Given sin A 12/13 and that angle A is in Quadrant I, find the exact value of cotA in simplest radical form using a rational denominator.

Answer 11

We can use the formula for cotangent in terms of sine and cosine:

cot A = cos A / sin A

Since sin A = 12/13 and A is in Quadrant I, we can use the Pythagorean theorem to find the value of the adjacent side of the triangle:

cos A = √(1 - sin^2 A) = √(1 - (12/13)^2) = √(1 - 144/169) = √(25/169) = 5/13

Now we can plug in the values for sine and cosine:

cot A = cos A / sin A = (5/13) / (12/13) = 5/12

Therefore, the exact value of cotA in simplest radical form using a rational denominator is 5/12.

Answer 12

Given Cot A - 2/5 and that angle A is in Quadrant I, find the exact value of sinA in simplest radical form using a rational denominator.

Answer 13

We can use the formula for cotangent in terms of sine and cosine:

cot A = cos A / sin A

Multiplying both sides by sine, we get:

cos A = cot A sin A

Substituting the given value of cot A = 2/5, we get:

cos A = (2/5) sin A

Since A is in Quadrant I, both sine and cosine are positive. Therefore, we can assume that:

sin A = k

cos A = √(1 - sin^2 A) = √(1 - k^2)

Substituting these values into the equation we got earlier, we get:

√(1 - k^2) = (2/5) k

Squaring both sides and moving all terms to one side, we get:

k^2 + (25/4) k^2 - 1 = 0

Solving this quadratic equation using the quadratic formula, we get:

k = (-25/8) ± √(625/64 + 4/4)
k = (-25/8) ± √(769/64)

Since sine is positive in Quadrant I, we take the positive square root:

k = (-25/8) + √(769/64)

We can simplify this expression by rationalizing the denominator:

k = (-25/8) + (√769)/(8√4)
k = (-25/8) + (√769)/16

Therefore, the exact value of sin A in simplest radical form using a rational denominator is:

sin A = k = (-25/8) + (√769)/16

Answer 14

i dont think that answer is correct

Answer 15

I apologize for the mistake in my previous answer. Let me correct it.

We are given that cot A = 2/5 and A is in Quadrant I. We can use the fact that cot A = cos A / sin A. Since A is in Quadrant I, both sine and cosine are positive, so we can assume that:

cos A = 2
sin A = 5

Now, using the Pythagorean identity, we have:

sin^2 A + cos^2 A = 1

Substituting the values we just found, we have:

5^2 + 2^2 = 1

25 + 4 = 29

So sin A = 5 / sqrt(29).

Therefore, the exact value of sin A in simplest radical form using a rational denominator is:

sin A = 5 / sqrt(29) * sqrt(29) / sqrt(29)

sin A = 5 sqrt(29) / 29

I hope this answer is helpful. Let me know if you have any further questions!