Math and Arithmetic

Trigonometry

# How do you solve 2 sin squared theta equals 1?

###### Wiki User

###### June 16, 2010 5:58AM

first divide each side by 2 so you get...

sine^2(X)=1/2

Then make sine ^2(X)=sine(x^2)

SO you get... sine(X^2)=1/2

Then take the sine^-1 of each side it will look like this X^2=sine^-1(1/2)

type the right side into a calc which will give you a gross decimal but it works (0.5235987756)

so now you have

X^2=0.5235987756

then take the square root of each side to make it linear and you will get X=.7236012546

and that is your answer!!!! make sure to check it on your calculator...I did and it worked

* * * * *

Not quite correct, I fear. Try this:

Let s = sin θ.

Then,

2s2 = 1;

s2 = ½; and

s = ±½√2.

Therefore,

θ = 45°, 135°, 225°, or 315°;

or, if you prefer,

θ = ¼π, ¾π, 1¼π, or 1¾π.

## Related Questions

###### Asked in Math and Arithmetic, Trigonometry

### If a cos theta plus b sin theta equals 8 and a sin theta - b cos theta equals 5 show that a squared plus b squared equals 89?

There is a hint to how to solve this in what is required to be
shown: a and b are both squared.
If
a cos θ + b sin θ = 8
a sin θ - b cos θ = 5
then square both sides of each to get:
a² cos² θ + 2ab cos θ sin θ + b² sin² θ = 64
a² sin² θ - 2ab sin θ cos θ + b² cos² θ = 25
Now add the two together:
a² cos² θ + a² sin² θ + b² sin² θ + b² cos² θ = 89
→ a²(cos² θ + sin² θ) + b² (sin² θ + cos² θ) = 89
using cos² θ + sin² θ = 1
→ a² + b² = 89

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### Sin equals 0.9?

###### Asked in Math and Arithmetic, Trigonometry

### How do you figure this out Sin theta equals -0.0138 so theta equals what?

Depending on your calculator, you should have an arcsin
function, which appears as sin^-1. It's usually a 2nd function of
the sin key. If you don't have this function, there are many free
calculators you can download... just google scientific calculator
downloads.
Anyway, this inverse function will give you theta when you plug in
the value of sin theta. Here's the algebra written out:
sin(theta)=-0.0138
arcsin(sin(theta))=arcsin(-0.0138)
theta=.......
The inverse function applied to both sides of the equation "cancels
out" the sin function and yields the value of the angle that was
originally plugged into the function, in this case theta. You can
use this principle to solve for theta for any of the other trig
functions:
arccos(cos(theta))=theta
arctan(tan(theta))=theta
and so on, but calculators usually only have these three inverse
functions, so if you encounter a problem using sec, csc, or cot,
you need to rewrite it as cos, sin, or tan.
sec=1/cos
csc=1/sin
cot=1/tan

###### Asked in Math and Arithmetic, Algebra, Trigonometry

### How do solve sin 2 theta - square root of 3 theta- equals 0?

The only real solution is theta = 0
For theta < 0 square root of 3 theta is not defined.
For theta > 0, sin theta increases slower than 3*theta and so
the sum is always negative.
The only real solution is theta = 0
For theta < 0 square root of 3 theta is not defined.
For theta > 0, sin theta increases slower than 3*theta and so
the sum is always negative.
The only real solution is theta = 0
For theta < 0 square root of 3 theta is not defined.
For theta > 0, sin theta increases slower than 3*theta and so
the sum is always negative.
The only real solution is theta = 0
For theta < 0 square root of 3 theta is not defined.
For theta > 0, sin theta increases slower than 3*theta and so
the sum is always negative.

###### Asked in Geometry, Brackets Parentheses and Quotation Marks

### How do you simplify bracket 1 plus tan theta bracket bracket 5 sin theta -2 bracket equals 0?

(in a past paper it asks u to solve this for
-180</=theta<180, so I have solved it)
Tan theta =-1, so theta = -45.
Use CAST diagram to find other values of theta for
-180</=theta<180:
Theta (in terms of tan) = -ve, other value is in either S or C.
But because of boundaries value can only be in S.
So other value= 180-45=135.
Do the same for sin.
Sin theta=2/5 so theta=23.6
CAST diagram, other value in S because theta (in terms of
sin)=+ve.
So other value=180-23.6=156.4.