If the terminal side of angle theta passes through point (-3, -4), what is the valuse of sec theta?
1) 5/3
2) -5/3
3)5/4
4)-5/4
Draw your triangle in standard position. Then you have
r=5
secθ = r/x = 5/-3
Well, if the terminal side of theta passes through (-3, -4), we can use the coordinates to find the value of sec theta. To do that, we need to find the hypotenuse of the right-angled triangle formed by the terminal side.
So, using the Pythagorean theorem, we have:
(-3)^2 + (-4)^2 = 9 + 16 = 25
This means that the hypotenuse is 5. Now, sec theta is equal to the hypotenuse divided by the adjacent side. Since the adjacent side is -3 (because the point is in the third quadrant), we have:
sec theta = 5 / -3
And if we simplify that fraction, we get:
sec theta = -5/3
So, the answer is option 2) -5/3. Now that's what I call a sec-culent punchline!
To find the value of sec(theta), we need to determine the value of the adjacent side of angle theta.
Since the terminal side of angle theta passes through point (-3, -4), we can determine the values of the adjacent side and the hypotenuse of the triangle formed.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse:
hypotenuse^2 = adjacent^2 + opposite^2
hypotenuse^2 = (-3)^2 + (-4)^2
hypotenuse^2 = 9 + 16
hypotenuse^2 = 25
hypotenuse = 5
Now that we know the length of the hypotenuse is 5, we can determine the value of the adjacent side. Since the point (-3, -4) lies in the third quadrant, the adjacent side will have a negative value.
Therefore, the value of sec(theta) is the ratio of the hypotenuse to the adjacent side:
sec(theta) = hypotenuse / adjacent
sec(theta) = 5 / -3
sec(theta) = -5/3
So, the correct answer is option 2) -5/3.
To determine the value of sec(theta), we need to find the length of the adjacent side and the length of the hypotenuse of the right triangle formed by the angle theta.
Given that the terminal side of angle theta passes through the point (-3, -4), we can use this information to find the lengths of the sides of the right triangle.
Let's first find the length of the hypotenuse:
The hypotenuse is the distance from the origin (0,0) to the point (-3, -4), which can be found using the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, x1 = 0, y1 = 0, x2 = -3, and y2 = -4.
distance = sqrt((-3 - 0)^2 + (-4 - 0)^2)
distance = sqrt(9 + 16)
distance = sqrt(25)
distance = 5
So, the length of the hypotenuse is 5.
Next, let's find the length of the adjacent side:
The adjacent side is the x-coordinate of the point (-3, -4).
In this case, the adjacent side is -3.
Now, we have the lengths of the adjacent side and the hypotenuse, which are -3 and 5, respectively. The secant of an angle is defined as the ratio of the hypotenuse to the adjacent side: sec(theta) = hypotenuse/adjacent.
Therefore, sec(theta) = 5/-3 = -5/3.
So, the correct answer is option 2) -5/3.