Find sin t,cos t and tan t when the terminal side of an angle of t radians passes through ( -3/5 , -4/5) on the unit circle.
find the hypotenuse: sqrt(9/25+16/25)=1
sinT= -4/5 / 1=-.8 and so on.
If csc theta is equals to negative and theta is in the 3rd quadrant?
a.find the other trigonometric function?
b.find the value ofthe angle?
To find the values of sin t, cos t, and tan t, we can use the coordinates of the point where the terminal side of the angle passes through the unit circle.
Given that the terminal side passes through the point (-3/5, -4/5), we can determine the corresponding values of sin t, cos t, and tan t.
Step 1: Determine the radius of the unit circle
Since the unit circle has a radius of 1 unit, the radius r of the circle passing through the given point can be calculated using the Pythagorean theorem:
r^2 = (-3/5)^2 + (-4/5)^2
r^2 = 9/25 + 16/25
r^2 = 25/25
r = 1
Step 2: Determine the values of sin t, cos t, and tan t
Since the radius of the circle is 1, the coordinates of the point (-3/5, -4/5) can be represented as (cos t, sin t).
Therefore, in this case:
cos t = -3/5
sin t = -4/5
To find the value of tan t, we can use the formula tan t = sin t / cos t.
tan t = (-4/5) / (-3/5) = 4/3
So, the values of sin t, cos t, and tan t when the terminal side of an angle of t radians passes through (-3/5, -4/5) on the unit circle are:
sin t = -4/5
cos t = -3/5
tan t = 4/3
To find the sine, cosine, and tangent of angle t when the terminal side of the angle passes through a point on the unit circle, we need to use the coordinates of that point.
In this case, the point is (-3/5, -4/5). Let's denote the x-coordinate of this point as x and the y-coordinate as y.
We know that the point (-3/5, -4/5) lies on the unit circle, which means that the distance from the origin to this point is 1. Using the Pythagorean theorem, we can calculate the length of the hypotenuse:
hypotenuse = √((-3/5)^2 + (-4/5)^2) = √(9/25 + 16/25) = √(25/25) = 1.
Now, we can calculate the value of sin t and cos t using the following formulas:
sin t = y / hypotenuse = (-4/5) / 1 = -4/5
cos t = x / hypotenuse = (-3/5) / 1 = -3/5.
Finally, we can calculate the value of tan t by dividing sin t by cos t:
tan t = sin t / cos t = (-4/5) / (-3/5) = 4/3.
Therefore, sin t = -4/5, cos t = -3/5, and tan t = 4/3.