I need to find the $\sin\theta$ when I am only given $\tan\theta = 1.936$
Thank your for any help. I am just having a hard time when I don't have examples to refer to with step-by-step directions. It's an online course. Some videos are helping but not for this particular example
thanks
More info :
Just asked to find the sin in decimal form which according to the answer sheet is 0.888
Best Answer
Draw a right triangle with one angle $\theta$ and the side adjacent to that having length !$1$. By the definition of tangent, the side opposite $\theta$ will have length $\tan \theta$.
The length of the hypotenuse, by the Pythagorean theorem is $$ \sqrt{1^2+\tan^2\theta} $$ Now $\sin\theta$ is the ratio of the opposite side to the hypotenuse, therefore $$ \sin\theta = \frac{\tan\theta}{\sqrt{1+\tan^2\theta}} $$ When $\tan\theta=1.936$, this gives $$\sin\theta = 0.888$$