Respuesta :
Answer:
[tex]\sin \theta = 0.9511[/tex] and [tex]\tan \theta = 3.078[/tex]
Step-by-step explanation:
Given that, [tex]\cos \theta = 0.309[/tex].
Now, we have to calculate the values of [tex]\sin \theta[/tex] and [tex]\tan \theta[/tex].
We know the identity that, [tex]\sin^{2}\theta + \cos^{2}\theta = 1[/tex]
So, [tex]\sin \theta = \sqrt{1 + \cos^{2}\theta} = \sqrt{1 - (0.309)^{2}} = 0.9511[/tex] {Since [tex]0 \leq \theta \leq 90^{\circ}[/tex]}
Now, [tex]\sec \theta = \frac{1}{\cos\theta} = \frac{1}{0.309} = 3.236[/tex]
Then, we know the identity, [tex]\sec^{2}\theta - \tan^{2}\theta = 1[/tex]
So, [tex]\tan \theta = \sqrt{\sec^{2}\theta - 1} = \sqrt{(3.236)^{2} - 1} = 3.078[/tex] (Answer) {Since [tex]0 \leq \theta \leq 90^{\circ}[/tex]}
