How do I solve this equation?
13.5=3.1sin(360/365(x-79.95)+12.18
the same way you solve any equation. Isolate x. First, of course balance your parentheses!
13.5=3.1sin(360/365(x-79.95))+12.18
3.1sin(360/365(x-79.95)) = 1.32
sin(360/365(x-79.95)) = 0.4258
360/365(x-79.95) = 25.20
x - 79.95 = 25.55
x = 105.50
To solve the equation 13.5 = 3.1sin(360/365(x-79.95)+12.18), you can follow these steps:
Step 1: Subtract 12.18 from both sides of the equation to isolate the sine term:
13.5 - 12.18 = 3.1sin(360/365(x-79.95))
Step 2: Simplify the left side:
1.32 = 3.1sin(360/365(x-79.95))
Step 3: Divide both sides by 3.1 to isolate the sine term:
1.32 / 3.1 = sin(360/365(x-79.95))
Step 4: Evaluate the inverse sine of both sides to solve for x:
sin^(-1)(1.32 / 3.1) = 360/365(x-79.95)
Step 5: Simplify the right side by multiplying both sides by (365/360):
(365/360)sin^(-1)(1.32 / 3.1) = x - 79.95
Step 6: Add 79.95 to both sides of the equation to isolate x:
(365/360)sin^(-1)(1.32 / 3.1) + 79.95 = x
Now, you have the solution for x in terms of trigonometric functions.
To solve the equation 13.5 = 3.1sin((360/365)(x-79.95) + 12.18), we can follow these steps:
Step 1: Simplify the equation if possible. In this case, we can simplify the expression (360/365)(x-79.95) + 12.18 by multiplying (360/365) by (x-79.95) and then adding 12.18.
Step 2: Rewrite the equation as 13.5 = 3.1sin(((360/365)(x-79.95)) + 12.18).
Step 3: Isolate the sine term by subtracting 12.18 from both sides of the equation: 13.5 - 12.18 = 3.1sin(((360/365)(x-79.95)).
Step 4: Calculate the value of the sine term. Divide both sides of the equation by 3.1: (13.5 - 12.18)/3.1 = sin(((360/365)(x-79.95)).
Step 5: Use the inverse sine function (sin^(-1)) to find the angle whose sine is equal to the value from step 4. Take the inverse sine of both sides of the equation: sin^(-1)((13.5 - 12.18)/3.1) = ((360/365)(x-79.95)).
Step 6: Solve for x. Multiply both sides of the equation by (365/360): (365/360) * sin^(-1)((13.5 - 12.18)/3.1) = x - 79.95.
Step 7: Add 79.95 to both sides of the equation to isolate x: ((365/360) * sin^(-1)((13.5 - 12.18)/3.1)) + 79.95 = x.
Now you have the solution for the equation. Simply calculate the right side of the equation to find the value of x.