For 90<theta<180, cos theta = -(5/13). Which is sin theta?
1. - sqrt 13/9
2. - sqrt 9/13
3. sqrt 9/13
4. sqrt 13/9
3?
sinØ = √(1 - (-5/13)^2) = .923 which is none of the choices
or
sketch a triangle in the 2nd quad,
x = -5
r = 13
x^2 + y^2 = r^2
25 + y^2 = 169
y^2 = 144
y = ± 12, but in quad II , y +12
so sinØ = 12/13 or appr .923 (same as above)
your choices:
1 and 2 are out, since they are negative
3. ---> √(9/13) ≠ .923
4. √(13/9) ≠ .923 , besides that result > 1, which would be impossible for the sine of any angle
Your question has no correct choices.
Sorry, I meant, "Which is sin theta/2?"
13^2 = 169
5^2 = 25
169-25 = 144
12^2 = 144
so:
cos T = -5/13
sin T = +12/13
T/2 will be in first quadrant
sin(T/2) = [(1-cos T)/2]^.5
= [ (1+5/13)/2]^.5
= [9/13]^.5
yes 3.
=
Thanks to both!
To find sin(theta) given that cos(theta) = -(5/13), we can use the Pythagorean identity for trigonometric functions.
The Pythagorean identity states that sin^2(theta) + cos^2(theta) = 1.
Since we know cos(theta) = -(5/13), we can now square it:
(cos(theta))^2 = (-(5/13))^2
cos^2(theta) = 25/169
Now, we can substitute this value into the Pythagorean identity:
sin^2(theta) + 25/169 = 1
Next, rearrange the equation to solve for sin^2(theta):
sin^2(theta) = 1 - 25/169
sin^2(theta) = (169/169) - (25/169)
sin^2(theta) = 144/169
Finally, take the square root of both sides to find the value of sin(theta):
sin(theta) = sqrt(144/169)
sin(theta) = 12/13
Therefore, the correct answer is 3. sqrt(9/13).