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tedrayoung1
28.07.2019 •
Mathematics
Will mark brainliest and give 16 points! (multiple choice but try to show steps)
1.given that 0∘≤c≤180∘, determine the value(s)
of ∠c to the nearest degree when sinc=0.9848.
a) 80°, 100°
b)100°
c)10°, 80°
d)80°
2. θ is an angle in standard position whose terminal arm is in
quadrant iv and cosθ=3/sqrt(13). find cscθ.
a)−2/sqrt(13)
b)−4/sqrt(13)
c)−sqrt(13)/2
d)sqrt(13)/4
3.if secθ=−52, and sinθ> 0, what is the value of tanθ?
a) −sqrt(21)/2
b)sqrt(−21)
c)−2 sqrt(21)/21
d)−5 sqrt(21/ 21
Solved
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Ответ:
1. The values of angle C to the nearest degree are 80° , 100° ⇒ (A)
2. csc Ф = -(√13)/2 ⇒ (C)
3. tan Ф = - (√21)/2 ⇒ (A)
Step-by-step explanation:
* Lets explain how to solve the problem
1.
∵ The measure of angle C is ⇒ 0° ≤ m∠C ≤ 180°
∴ ∠C lies in the first quadrant or in the second quadrant
∴ m∠C = Ф OR m∠C = 180 - Ф, where Ф is an acute angle
∵ sin∠C = 0.9848
∴ sin Ф = 0.9848
- Use the inverse function sin^-1 to find Ф
∴ Ф = sin^-1 0.9848
∴ Ф ≅ 80°
- Lets find ∠C
∵ m∠C = Ф
∴ m∠C = 80°
∵ m∠C = 180° - Ф
∴ m∠C = 180 - 80 = 100°
* The values of angle C to the nearest degree are 80° , 100°
2.
- The terminal arm of angle Ф is in quadrant IV
∵ In quadrant IV sin Ф , csc Ф , tan Ф , cot Ф are negative values
∵ In quadrant IV cos Ф , sec Ф are positive values
∵ cos Ф = 3/√13
∵ csc Ф = 1/(sin Ф)
- Lets use the identity sin²Ф + cos²Ф = 1 to find sin Ф
∵ sin²Ф + (3/√13)² = 1
∴ sin²Ф + 9/13 = 1 ⇒ subtract 9/13 from both sides
∴ sin²Ф = 4/13 ⇒ take √ for both sides
∵ sin Ф = ± 2/√13
- The value of the sin the IV quadrant is negative
∴ sin Ф = - 2/√13
∵ csc Ф = 1/sin Ф
∴ csc Ф = -(√13)/2
3.
∵ sec Ф = -5/2 and sin Ф > 0
∵ sec Ф = 1/cos Ф
- The value of cos Ф is negative and the value of sin Ф is positive,
then Ф lies in the second quadrant
∵ In the second quadrant cos Ф , sec Ф , tan Ф , cot Ф are negative
values but sin Ф and csc Ф are positive values
- Lets use the identity tan²Ф + 1 = sec²Ф to find tan Ф
∵ sec Ф = -5/2
∵ tan²Ф + 1 = sec²Ф
∴ tan²Ф + 1 = (-5/2)²
∴ tan²Ф + 1 = 25/4 ⇒ subtract 1 from both sides
∴ tan²Ф = 21/4 ⇒ take √ for both sides
∴ tan Ф = ± √21/2
∵ Ф lies in the second quadrant
∴ tan Ф = - (√21)/2
Ответ:
The answer to your question is:
Part A: x₁ = 3 x₂ = -5/4
Part B. Vertex = (7/8, - 18.06)
Step-by-step explanation:
Data
4x² - 7x - 15
Part A. Factor the expression given to find the x - intercepts.
- Multiply 4 by -15 = -60
- Find the prime factors of -60
-60 2
-30 2
- 15 3
-5 5
-1
- Find to numbers that add them up give -7
these numbers are -12 and + 5
4x² - 12x + 5x - 15
4x(x - 3) + 5(x - 3)
(x - 3)(4x + 5)
- Equal each term to zero to find the x-intercepts
x₁ = 3 x₂ = -5/4
Part B. The vertex is a minimum
y = 4x² - 7x - 15
y + 15 + 4(7/8)² = 4(x² - 7/4 x + (7/8)²)
y + 289/16 = 4( x - 7/8)²
Vertex = (7/8, - 18.06)
Part C.
1.- Plot the the vertex
2.- Plot the x- intercepts
3.- Join the points