Trigonometric Identity for Tangent
The tangent of an angle ($A$) in trigonometry is defined as the ratio of the sine of the angle to the cosine of the angle. This fundamental relationship is expressed as:
$ \tan A = \frac{\sin A}{\cos A} $
Calculating tan A
We are given the following values:
- $\sin A = 0.6$
- $\cos A = 0.8$
Substitute these values directly into the trigonometric identity:
$ \tan A = \frac{0.6}{0.8} $
To simplify the calculation, we can remove the decimal points by multiplying the numerator and denominator by 10:
$ \tan A = \frac{6}{8} $
Now, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
$ \tan A = \frac{6 \div 2}{8 \div 2} = \frac{3}{4} $
Finally, convert the fraction to its decimal form:
$ \tan A = 0.75 $
Result
The value of $\tan A$ is 0.75.
Similar Questions
- If $\sin(x) = 0.6$ and $x \in (0, \pi/2)$, find $\sin(2x) + \cos(2x)$.
- If $\cos A = 1 - 2\sin^2A$, then what is the value of $\cos 2A$?
- If $\sin(3x + 10^{\circ}) = \cos(2x - 5^{\circ})$, find x.
- If $\sin(A) = \cos(B), \cos(A) = \sin(C)$, and $A + B + C = 90^\circ$, then what is the value of angle A?
- A triangle has sides 8 cm and 10 cm, and the angle between them is $120^\circ$. What is its area?
- If $\sin A = 0.6$, what is the value of $\tan A$ ?
- If $\sec A + \tan A = p$, then what is $\sec A$ in terms of p?
- Which of the following is true for all acute angles A?
- If $\tan x = \cot(3x - 30^\circ)$, find $x$.
Important Questions from Trigonometry
The given equation can be reduced to
If sin2x = a - b√c, where a and b are natural numbers and c is prime number, then what is the value of a - b + 2c ?
Let θ be a positive angle. If the number of degrees in θ is divided by the number of radians in θ, then an irrational number 180 / π results. If the number of degrees in θ is multiplied by the number of radians in θ, then an irrational number 125π / 9 results. The angle θ must be equal to
What is sin 2α equal to?
If \(\sin θ = \frac{8}{{17}}\) , then find the value of tan θ.
