If I know that sin ( θ ) = 12/13 I can use the Pythagorean theorem to find that cos ( θ ) = 5/13 . What is tan ( θ )?
Never mind I got the answer. Its 12/5.
sin (x) = 12/13 this is because sine is opposite divided by hypotenuse.
cos (x) = 5/13 this is because cosine is adjacent divided by hypotenuse.
tan (x) = 12/5 this is because tangent is opposite divided by adjacent.
Yes
You might also remember that
tan x = sin x / cos x
To find tan (θ), we can use the formula:
tan(θ) = sin(θ) / cos(θ)
Given that sin(θ) = 12/13 and cos(θ) = 5/13, we can substitute these values into the formula:
tan(θ) = (12/13) / (5/13)
Now, we can simplify the expression:
tan(θ) = (12/13) * (13/5) [dividing fractions is equivalent to multiplying by the reciprocal]
= 12/5
Therefore, tan(θ) = 12/5.
To find the value of tan(θ) given that sin(θ) = 12/13 and cos(θ) = 5/13, you can use the trigonometric identity tan(θ) = sin(θ) / cos(θ).
Since you already know sin(θ) = 12/13 and cos(θ) = 5/13, plug these values into the formula for tan(θ):
tan(θ) = sin(θ) / cos(θ)
= (12/13) / (5/13)
= 12/13 * 13/5
= 12/5
Therefore, the value of tan(θ) is 12/5.