The value of [tex]\tan(\theta)[/tex] is -35/12
Trigonometry ratios are used to determine the sides and angles in a right triangle
The trigonometry ratio is given as:
[tex]\sec(\theta) = -\frac{37}{12}[/tex]
Calculate the cosine of the angle
[tex]\cos(\theta) = -\frac{12}{37}[/tex]
Calculate the sine of the angle using
[tex]\sin(\theta) = \sqrt{1 - \cos^2(\theta)}[/tex]
So, we have:
[tex]\sin(\theta) = \sqrt{1 - (-12/37)^2}[/tex]
[tex]\sin(\theta) = \sqrt{1 - (144/1369}[/tex]
Evaluate
[tex]\sin(\theta) = \pm\sqrt{\frac{1225}{1369}}[/tex]
Evaluate
[tex]\sin(\theta) = \pm\frac{35}{37}[/tex]
The sine of an angle is positive between [tex]\pi/2[/tex] and [tex]\pi[/tex].
So, we have:
[tex]\sin(\theta) = \frac{35}{37}[/tex]
The tangent is then calculated as:
[tex]\tan(\theta) = \sin(\theta) \div \cos(\theta)[/tex]
This gives
[tex]\tan(\theta) = \frac{35}{37} \div \frac{-12}{37}[/tex]
Divide
[tex]\tan(\theta) = -\frac{35}{12}[/tex]
Hence, the value of [tex]\tan(\theta)[/tex] is -35/12
Read more about trigonometry ratios at:
https://brainly.com/question/10417664
