Problem
If $\tan t=-\frac{7}{24}$ and $\frac{\pi}{2}
Solution
Step 1 ：Given that \( \tan t = -\frac{7}{24} \) and \( \frac{\pi}{2} < t < \pi \), we know that we are in the second quadrant where sine is positive and cosine is negative.
Step 2 ：We can use the Pythagorean identity \( \sin^2 t + \cos^2 t = 1 \) to find the values of \( \sin t \) and \( \cos t \).
Step 3 ：Once we have these, we can find the values of \( \sec t, \csc t, \cot t \) using their definitions in terms of sine and cosine.
Step 4 ：The final answer is: \( \sin t = \boxed{0.28} \), \( \cos t = \boxed{-0.96} \), \( \sec t = \boxed{-1.0416666666666667} \), \( \csc t = \boxed{3.571428571428571} \), \( \cot t = \boxed{-3.4285714285714284} \).
From Solvely APP
Solution
Step 1 ：Given that \( \tan t = -\frac{7}{24} \) and \( \frac{\pi}{2} < t < \pi \), we know that we are in the second quadrant where sine is positive and cosine is negative.
Step 2 ：We can use the Pythagorean identity \( \sin^2 t + \cos^2 t = 1 \) to find the values of \( \sin t \) and \( \cos t \).
Step 3 ：Once we have these, we can find the values of \( \sec t, \csc t, \cot t \) using their definitions in terms of sine and cosine.
Step 4 ：The final answer is: \( \sin t = \boxed{0.28} \), \( \cos t = \boxed{-0.96} \), \( \sec t = \boxed{-1.0416666666666667} \), \( \csc t = \boxed{3.571428571428571} \), \( \cot t = \boxed{-3.4285714285714284} \).
