I'm having trouble doing trigonometry.
Determine the possible coordinates of a terminal point for each angle in standard position.
A) 315°
I have no clue how to do this. Please explain and show me the work so I can do the rest of the questions myself
if the radi is 1, then
1@315=sin315+jcos315= -0.707+j.707
And if I choose 4 as the radi. Then would it be:
sin (315°)= y/4
4 sin (315°)= -2.8284
So that is the y value.
Cos (315°) = x/4
4 cos (315°) = 2.8284
So that is the x value
?
Where are you measuing the angle from, and in which direction? It makes all the difference. If you are measuring from the positive x axis, counterclockwise, yes, x will be positve, and y will be negative, as you did above
My example was measuring the angle from the j (y axis), clockwise.
You
In trig we consider the positive x-axis to have a direction of 0 degrees (or radians) and consider counterclockwise to be a positive rotation, so
East -- 0
North -- 90
West -- 180
South -- 270
So for a unit circle of radius 1, any point
(x,y) can be labelled (cosθ , sinθ)
so for your angle of 135 degrees, we could have (cos135, sin135)
or
(-sqrt(2)/2 , 1/2)
bobpursley gave you -0.707+j.707
which is the same thing expressed as a vector.
multiply the x and y coordinates by the same number would simply change the length of your radius.
To determine the coordinates of a terminal point for an angle in standard position, we can use the unit circle. The unit circle is a circle with a radius of 1 unit, centered at the origin (0, 0) of a coordinate system.
To determine the coordinates of a terminal point for an angle, we follow these steps:
1. Convert the angle to radians: To convert an angle from degrees to radians, we use the formula: radians = (angle in degrees) x (π/180).
For example, to convert 315 degrees to radians: radians = 315 x (π/180) ≈ 5.5 radians.
2. Use the coordinates of the unit circle: On the unit circle, the x-coordinate represents the value of the cosine of the angle, and the y-coordinate represents the value of the sine of the angle.
For angle 315 degrees (or 5.5 radians):
- The cosine of 5.5 radians is the x-coordinate of the terminal point.
- The sine of 5.5 radians is the y-coordinate of the terminal point.
To find these values, we can use a calculator or reference tables specifically designed for trigonometric functions.
3. Determine the coordinates:
- The x-coordinate is the cosine of 5.5 radians.
- The y-coordinate is the sine of 5.5 radians.
Using a calculator, cosine(5.5) is approximately -0.71 and sine(5.5) is approximately -0.71.
Thus, the possible coordinates of the terminal point for an angle of 315 degrees are approximately (-0.71, -0.71).
I hope this explanation helps you understand how to determine the coordinates of a terminal point. Feel free to apply this method to the other angles.