4+29sin=12cos^2
How do you determine this
If your expression mean:
4+29sin(x)=12cos^2(x)
then go on:
wolframalpha dot com
When page be open in rectangle type:
solve 4+29sin(x)=12cos^2(x)
and click option =
After few seconds when you see result click option: Show steps
Remark:
cos ^ 2 ( x ) = 1 - sin ^ 2 ( x )
12 cos ^ 2 ( x )= 12 [ 1 - sin ^ 2 ( x ) ] =
12 - 12 sin ^ 2 ( x )
29 sin ( x ) - 12 cos ^ 2 ( x ) + 4 =
29 sin ( x ) - [ 12 - 12 sin ^ 2 ( x ) ] + 4 =
29 sin ( x ) - 12 + 12 sin ^ 2 ( x ) + 4
= 29 sin ( x ) - 8 + 12 sin ^ 2 ( x ) =
12 sin ^ 2 ( x ) + 29 sin ( x ) - 8
When I solved this out I got x=-32/12 and x=1/4. Is this right?
Not x = .... but rather sinx = -32/12 or sinx = 1/4
Picking up from where Bosnian left off
12sin^2 x+ 29sinx - 8 = 0
(4sinx - 1)(3sinx + 8) = 0
sinx = 1/4 or sinx = -8/3, but sinx has to be between -1 and 1, so the last part is undefined
sinx = 1/4, so
x = 14.48° or 165.52°
if you want radians, set your calculator to RAD
and find arcsin (.25)
To solve the given equation, 4 + 29sin(x) = 12cos^2(x), you need to use trigonometric identities and algebraic manipulation. Here's a step-by-step explanation of how to determine the solution:
Step 1: Use the identity cos^2(x) = 1 - sin^2(x) to rewrite the equation as 4 + 29sin(x) = 12(1 - sin^2(x)).
Step 2: Distribute 12 to both terms to get 4 + 29sin(x) = 12 - 12sin^2(x).
Step 3: Rearrange the equation to form a quadratic equation: 12sin^2(x) + 29sin(x) - 8 = 0.
Step 4: Factor the quadratic equation: (3sin(x) - 1)(4sin(x) + 8) = 0.
Step 5: Set each factor equal to zero individually and solve for sin(x).
- 3sin(x) - 1 = 0 --> 3sin(x) = 1 --> sin(x) = 1/3
- 4sin(x) + 8 = 0 --> 4sin(x) = 8 --> sin(x) = 2
Step 6: Check the solutions in the original equation to see if they are valid. Plugging sin(x) = 1/3 back into the equation, we get 4 + 29(1/3) = 12(1 - (1/3)^2), which simplifies to 13 = 11. Since the equation is not satisfied, sin(x) = 1/3 is not a valid solution.
Step 7: Therefore, the only valid solution is sin(x) = 2. However, this is not possible since the values of sine range between -1 and 1. Therefore, there are no solutions to the given equation.
Final Answer: The given equation 4 + 29sin(x) = 12cos^2(x) has no solutions.