Find theta in degrees and radians?

Question

Find the acute angle theta in degrees and radians without a calculator

sec theta = 2

thanks in advance

Answer 1

The secant ratio is the reciprocal of the cosine. Substituting this in gives you:
1 / (cos Θ) = 2. Multiplying by cos Θ,
1 = 2 cos Θ. Dividing by 2,
1 / 2 = cos Θ.

This means Θ is ±30°, depending on whether Θ lies in Quadrant I or IV.
±30°(π / 180°) = ±π / 6 radians.

Answer 2

Convert Theta To Degrees

Answer 3

cos theta = 1 csc theta so cos theta = 1/2
Thus theta = 60 degrees = pi/3 radians

Answer 4

Use proportions to convert Radian to degree.

D = angle measured in degrees.
R = angle measured in radians.

D = 180 times Pi/180. R = Pi/180. A long time ago someone figured out that the circumference of a circle is a bit more then three times the diameter. About 3.14 times. The exact value is 22/7.

Answer 5

for simplicity : theta = X
You must know that sec(x) = 1/cos(x) to solve this problem.

sec(X) = 2
1/cos(X) = 2
cos(x) = 1/2
x = arccos(1/2)
x = 60 degrees

to change from degrees to radians do the following:

60 deg * (Pi rad/180 deg)
So in radians the answer becomes Pi/3

Answer 6

that means that sin theta is 1/2 since sec is i over sin
thats 30 in degrees you have to memorize that or get it using the triangles
to get it in radians you just put a pi in front of the number and a 180 under it
thats 30pi/180 which is pi/6

Answer 7

Radians are the "natural" unit for angle measure. Use radians unless told otherwise. In Calculus especially, many formulas do not work if you don't use radians.

Answer 8

cos theta = 1/2
theta = pi/3 = 60 degrees
or
theta = 5pi/3 = 300 degrees

Answer 9

sec means 1/cos

1/cos(theta) = 2

cos (theta) = 1/2

theta = pi/3 (must know)
degrees = 60

Answer 10

You have:
sec (θ) = 2

Remember the definition of sec:
sec (θ) = 1/cos(θ)

Thus:
1/cos(θ) = 2

Solving for cos(θ):
cos(θ) = ½

If you remember your geometry for a 30-60-90 triangle, and the rule of SOH-CAH-TOA:

cos(60˚) = adjacent / hypotenuse = ½

.........../|
........./..|
......./....|
...../......|
.1./.......|
../.........|
/60____|
.... ½

Therefore:
θ = 60˚

To convert to radians, multiply by π/180
θ = 60 * (π/180)
θ = π/3

Another way to get the answer in radians is to remember that a full circle is 360˚ or 2π radians. One sixth of that is:
30˚ and π/3 radians.