Trigonometry: Calculate Tan A from Sin A
This solution determines the value of
$tan A$given
$\sin A = 0.6$.
Solution Steps
-
Use Pythagorean Identity
$\sin^2 A + \cos^2 A = 1$.
-
Calculate
$\cos A$:
Using the identity,
$\cos^2 A = 1 - \sin^2 A$.
Substitute
$\sin A = 0.6$:
$\cos^2 A = 1 - (0.6)^2 = 1 - 0.36 = 0.64$.
Assuming
$A$is an acute angle,
$\cos A = \sqrt{0.64} = 0.8$.
-
Calculate
$\tan A$:
Use the ratio
$\tan A = \frac{\sin A}{\cos A}$.
Substitute the values of
$\sin A$and
$\cos A$:
$\tan A = \frac{0.6}{0.8} = \frac{6}{8} = \frac{3}{4}$.
$\tan A = 0.75$.
The value of
$tan A$is 0.75.
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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.
