1. Write the algebraic expression which shows Cos((ArcSin(4/X)),
2. Angle If Csc(-Θ)=15/4?
2. - what quadrant is it in, find the sin(-Θ), Sin(Θ), Tan(90deg-Θ), Tan(Θ), csc(Θ), Sec(-Θ+360deg), Thanks
You have to be kidding. What did you do with my other response?
I suspect you will get no where until you do what I suggested.
1. To write the algebraic expression for Cos((ArcSin(4/X)), we can start by understanding the identities involved.
The arc sine function (ArcSin) returns the angle whose sine is a given value. So, ArcSin(4/X) represents the angle whose sine is equal to 4/X.
Then, we take the cosine of this angle using the Cos function. Therefore, the algebraic expression is:
Cos((ArcSin(4/X)))
2. To find the angle if Csc(-Θ) = 15/4, we first need to understand the properties of the cosecant function (Csc). The cosecant of an angle is equal to the reciprocal of the sine of that angle.
So, we have Csc(-Θ) = 15/4, which means that the reciprocal of the sine of -Θ is equal to 15/4.
To determine the quadrant in which this angle lies, we need to consider the signs of the trigonometric ratios for different angles in each quadrant.
Since Csc(-Θ) is positive (15/4 is positive), we know that sine is positive.
In the first quadrant (0 to 90 degrees), sine is positive, and tangent is positive. In the second quadrant (90 to 180 degrees), sine is positive, and tangent is negative. In the third quadrant (180 to 270 degrees), sine is negative, and tangent is positive. In the fourth quadrant (270 to 360 degrees), sine is negative, and tangent is negative.
Since sine is positive in this case, the angle lies in either the first or second quadrant. To determine which quadrant, we need additional information.
Sin(-Θ) is equal to the negative of sin(Θ) in any quadrant. Therefore, if sin(-Θ) = sin(Θ), the angle is in the first quadrant. If sin(-Θ) = -sin(Θ), the angle is in the second quadrant.
To find the values of sin(-Θ), sin(Θ), tan(90deg-Θ), tan(Θ), csc(Θ), and sec(-Θ+360deg), we need to know the exact value of Θ or have additional information.