1.Find the missing values given that Ø in degrees=270.
2.Find the missing values given that Ø in degrees=270.
I can find the radians but not sin,cos,sec,tan,csc,cot i really need help
this angle is just a vertical line. So only sin,cos,cot,csc are defined.
Draw the angle.
Recall that r is always positive.
sin = y/r
cos = x/r
tan = y/x
and so on.
Ok can you work sin for me
To find the missing values for the trigonometric functions (sin, cos, sec, tan, csc, cot) given that Ø (theta) is equal to 270 degrees, we need to first convert 270 degrees to radians.
1. Converting degrees to radians:
To convert degrees to radians, we use the following formula:
radians = degrees * π / 180
Substituting 270 degrees into the formula:
radians = 270 * π / 180
Simplifying the expression:
radians = 3π/2
So, Ø in radians is equal to 3π/2.
2. Calculating trigonometric values:
To find the missing trigonometric values, we will use the unit circle and its coordinates. The unit circle is a circle with a radius of 1 unit, centered at the origin (0,0) in a coordinate plane.
For Ø = 270 degrees (3π/2 radians), the point on the unit circle will have x-coordinate = 0 and y-coordinate = -1.
Using these coordinates, we can find the values for each trigonometric function:
- Sine (sin): sin(Ø) = y-coordinate on the unit circle = -1
- Cosine (cos): cos(Ø) = x-coordinate on the unit circle = 0
- Secant (sec): sec(Ø) = 1 / cos(Ø)
Since cos(Ø) = 0, sec(Ø) is undefined (division by zero is not allowed).
- Tangent (tan): tan(Ø) = sin(Ø) / cos(Ø)
Since cos(Ø) = 0, tan(Ø) is also undefined (division by zero).
- Cosecant (csc): csc(Ø) = 1 / sin(Ø)
Since sin(Ø) = -1, csc(Ø) is -1/-1 = 1.
- Cotangent (cot): cot(Ø) = 1 / tan(Ø)
Since tan(Ø) is undefined, cot(Ø) is also undefined.
Therefore, the missing values for Ø = 270 degrees are:
- sin(Ø) = -1
- cos(Ø) = 0
- sec(Ø) = undefined
- tan(Ø) = undefined
- csc(Ø) = 1
- cot(Ø) = undefined.