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Anit [1.1K]
3 years ago
5

Find the exact value of sec(–135°).

Mathematics
1 answer:
MA_775_DIABLO [31]3 years ago
6 0

Answer: -\sqrt{2}

Step-by-step explanation:

The trigonometric function secant is the reciprocal of cosine:

sec(\alpha)=\frac{1}{cos(\alpha)}

For -135\°:

sec(-135\°)=\frac{1}{cos(-135\°)} (1)

On the other hand, it is known cos(-\alpha)=cos(\alpha), hence:

cos(-135\°)=cos(135\°) (2)

In addition, it is known cos(135\°)=-cos(45\°)=-\frac{\sqrt{2}}{2} (3)

Substituting this on (1):

sec(-135\°)=\frac{1}{-\frac{\sqrt{2}}{2}} (4)

sec(-135\°)=-\frac{2}{\sqrt{2}} (5)

sec(-135\°)=-\frac{2}{\sqrt{2}}(\frac{\sqrt{2}}{\sqrt{2}}) (6)

Finally:

sec(-135\°)=-\sqrt{2}

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A gentleman is standing 10 feet from a streetlight. He is 5'6 tall and has a shadow of 24 feet. What is the height of the street
Goshia [24]

Answer:

Height of the streetlight ≈ 8 ft(nearest foot)

Step-by-step explanation:

The doc file displays the triangle formed from the illustration. x is the height of the street light. The distance from the gentle man to the street light is 10 ft. He  has a height of 5.6 ft  and the shadow formed on the ground is 24 ft long. The height of the street light can be calculated below.

The length of the tip of the shadow to the base of the street light is 34 ft. Similar triangle have equal ratio of their corresponding sides .

ab = 5.6 ft

The ratio of the base sides = 24/34

The ratio of the heights = 5.6/x

The two ratio are equal Therefore,

24/34 = 5.6/x

24x = 5.6 × 34

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Download docx
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3 years ago
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3 years ago
Find the approximate solution(s) to each of the following equations graphically. Use technology to support your
ser-zykov [4K]

Answer: x" = 5.69

Step-by-step explanation:

The graphic solution is attached.

Verifying the solution:

Existence condition: x > 0

2x - 4 = √x + 5

√x =2x - 4 - 5

√x =2x - 9 (²)

x = (2x - 9)²

x = 4x² - 36x + 81

4x² - 36x - x + 81 = 0

4x² - 37x + 81 = 0

Δ = -37² - 4.4.81 = 1369 - 1296 = 73

x = 37 ±√73/8                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          

x' = 3.55

x" = 5.69

checking:

2*3.55 - 4 = 3.1

√3.55 + 5 = 6.88 Its not the same ∴ 3.55 is not a solution

2*5.69 - 4 = 7.39

√5.69 + 5 = 7.39 ∴ it's the only solution

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