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3 years ago

Y + 5 = -x Slope intercept

Mathematics

1 answer:

Arturiano [62]3 years ago

3 0

The slope intercept form is y=-x-5

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Let (6,-5) be a point on the terminal side of θ. Find the exact values of sin θ, sec θ, and tan θ.

makvit [3.9K]

Answer:

sinθ = -5/√61

secθ = √61/6

tanθ = -5/6

Step-by-step explanation:

From the given coordinate (6, -5), x = 6 and y = -5. This shows that the point lies in the 4th quadrant. In the fourth quadrant, only cos θ is positive, both sin θ and tan θ are negative.

Let us get the value of the radius 'r' first before calculating the trigonometry identities.

Using the Pythagoras theorem;

$r^2 = x^2 + y^2\\r^2 = 6^2 + (-5)^2\\r^2 = 36+25\\r^2 = 61\\r = \sqrt{61}$

Using SOH, CAH, TOA to get the trigonometry identities;

Given x = 6, y =5 and r = √61

$sin \theta = opp/hyp = y/r\\sin \theta = 5/\sqrt{61} \\$

Since sin θ, is negative in the fourth quadrant, $sin \theta = -5/\sqrt{61} \\$

$cos \theta = adj/hyp = x/r\\cos \theta = 6/\sqrt{61} \\$

$sec \theta = \frac{1}{cos \theta} \\sec \theta = \frac{1}{6/\sqrt{61} } \\sec \theta = \frac{\sqrt{61} }{6}$

For tanθ:

$tan \theta = \frac{opp}{adj} = \frac{y}{x} \\tan \theta = \frac{5}{6}\\$

Since tan θ, is negative in the fourth quadrant, $tan \theta = -5/6$

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4 years ago

Which of the 3 is the answer?

lbvjy [14]

9 ^2 is the answer for this question

6 0

3 years ago

The length of a rectangular prism is four times the width. The height of the prism is 8 ft. If the volume of the prism is 160 ft

myrzilka [38]

Answer: w=rt5 approx. 2.2

Step-by-step explanation:

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3 years ago

Which of the following is equivalnt to √20

Elodia [21]

2✓5.
In decimal form, it's 4.5.

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4 years ago

Ms. Lorahs smartphone has 3.5 GB of free storage space, which is 27.5% of the total storage space on her smartphone. What is the

statuscvo [17]

12.73 GB total when rounded to the nearest 100th.

3.5/27.5=y

y•100= 12.73

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3 years ago