3 years ago

The point (-7,4) in on the terminal side of an angle t. Find sec (t) to two decimal places.

Mathematics

1 answer:

Sliva [168]3 years ago

6 0

Answer:

-1.15

Step-by-step explanation:

The tangent of the angle can be found as ...

tan(t) = (y-coordinate)/(x-coordinate) = -4/7

The secant of the angle is related by ...

sec(t)² = tan(t)² +1 = (-4/7)² +1 = 65/49

Then the secant of this 2nd-quadrant angle is ...

sec(t) = -√(65/49) = -(√65)/7 ≈ -1.15

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Yuki888 [10]

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3 years ago

Find the distance between (2a+2, 2b) and (2b+2, 2a), given that a>b.

Elina [12.6K]

Answer:

Distance = $2\sqrt{2}a-2\sqrt{2}b$

Step-by-step explanation:

We will use distance formula shown below to solve this:

Distance Formula: $\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

Where

x_1 = 2a + 2

y_1 = 2b

x_2 = 2b+2

y_2 = 2a

Substituting, we solve for the expression for distance:

$D=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\\D=\sqrt{(2a-2b)^2+((2b+2)-(2a+2))^2}\\D=\sqrt{(2a-2b)^2+(2b+2-2a-2)^2}\\D=\sqrt{(2a-2b)^2+(2b-2a)^2}\\D=\sqrt{4a^2 -8ab+4b^2+4b^2-8ab+4a^2}\\D=\sqrt{8a^2-16ab+8b^2}\\D=\sqrt{(2\sqrt{2}a-2\sqrt{2}b)^2}\\D=2\sqrt{2}a-2\sqrt{2}b$