Question

Given that secant theta = Negative StartFraction 37 Over 12 EndFraction, what is the value of cotangent theta, for StartFraction pi Over 2 EndFraction less-than theta less-than pi

Answer 1

$cot\theta$  $=\frac{12}{35}$

Step-by-step explanation:

$sec\theta =\frac{37}{12}$

⇔$\frac{1}{cos \theta} =\frac{37}{12}$

⇔$cos \theta = \frac{12}{37}$

we know that

$sin \theta = \sqrt{1-cos^2\theta}$

$sin\theta =\sqrt{1-(\frac{12}{37})^2 }$

$sin\theta=\sqrt{\frac{1225}{1369} }$

$sin\theta = \frac{35}{37}$

Therefore $cot\theta =\frac{cos\theta}{sin\theta}$  $=\frac{\frac{12}{37} }{\frac{35}{37} }$  $=\frac{12}{35}$  , for $\frac{\pi}{2} <\theta<\pi$

Answer 2

Answer:

i'm not sure but it might be -12/35

Step-by-step explanation: