solve the equation for the range zero degrees less than or equal to theta less than or equal to 360 degrees.
4 sin 0=-1
4sinØ = -1, 0° ≤ Ø ≤ 360°
sinØ = -1/4
my calculator gives me Ø = -14.48°
but that is outside our domain
Here is how I do those types:
Since sinØ is negative, I know that my angle Ø must be in quadrants III or IV
so I use sinØ = +1/4 to get +14.48°
in quad III we have 180+14.48 = 194.48°
in quad IV we have 360-14.48 = 345.52°
check these answers with your calculator, they both work
Also notice that -14.48° is co-terminal with 345.52°,
your calculator is programmed to give you the angle closest to zero , which would be -14.48°
I wanted to help u by solving this question..
So, first of all we need to do is... understand the question & then i literally dont know the solution #wasted
To solve the equation 4sin(θ) = -1 for the range 0 degrees ≤ θ ≤ 360 degrees, we can follow these steps:
Step 1: Divide both sides by 4
sin(θ) = -1/4
Step 2: Find the angle that has a sin value of -1/4
Remember that sin(θ) = y/r, where y represents the opposite side and r represents the hypotenuse in a right triangle. Since the sin value is negative, the angle should be in the third or fourth quadrant.
Step 3: Use a calculator to find the angle
Using a calculator, you can find the angle whose sin value is -1/4 by taking the inverse sine of -1/4. This can be denoted as sin^(-1)(-1/4) or asin(-1/4).
Step 4: Calculate the angle in degrees.
The calculator will give you the value in radians, but you can convert it to degrees using the conversion formula: Degrees = (radians * 180) / π.
So, by following these steps, you can find the angle in the given range for which sin(θ) = -1/4.
To solve the equation 4sin(theta) = -1 for the given range, we need to find the values of theta that satisfy the equation.
Step 1: Divide both sides of the equation by 4:
sin(theta) = -1/4
Step 2: Take the inverse sine (or arcsine) of both sides to find the angle theta:
theta = arcsin(-1/4)
Step 3: Use a calculator to find the arc sine value of -1/4. This will give you the principal value of theta.
Using a calculator, arcsin(-1/4) is approximately -14.48 degrees.
Step 4: However, the given range is from 0 degrees to 360 degrees.
Since the sine function has a period of 360 degrees, we can add or subtract 360 degrees to the principal value multiple times to find all the possible angles within the given range.
Adding 360 degrees to the principal value of -14.48 degrees gives us:
theta = -14.48 + 360 = 345.52 degrees
Adding another 360 degrees gives us:
theta = 345.52 + 360 = 705.52 degrees
Since 705.52 degrees is outside the given range, we discard it.
Step 5: Therefore, the solution to the equation for the given range is:
theta = -14.48 degrees and 345.52 degrees.