\& Determine an angle between $90^{\circ}$ and $180^{\circ}$ that has each trigonometric function value. Write the angle to the nearest degree.
a) $\sin \theta=0.42$
b) $\tan \theta=-0.35$
c) $\cos \theta=-0.58$
d) $\tan \theta=-1.25$
e) $\cos \theta=-0.45$
f) $\sin \theta=0.75$

Step 1 ：\(\text{a) Since sine is positive in the second quadrant, we can find the angle using the arcsin function and then subtract it from } 180^\circ\text{.}\)

Step 2 ：\(\text{b) Since tangent is negative in the second quadrant, we can find the angle using the arctan function and then add it to } 90^\circ\text{.}\)

Step 3 ：\(\text{c) Since cosine is negative in the second quadrant, we can find the angle using the arccos function.}\)

Step 4 ：\(\text{d) Since tangent is negative in the second quadrant, we can find the angle using the arctan function and then add it to } 90^\circ\text{.}\)

Step 5 ：\(\text{e) Since cosine is negative in the second quadrant, we can find the angle using the arccos function.}\)

Step 6 ：\(\text{f) Since sine is positive in the second quadrant, we can find the angle using the arcsin function and then subtract it from } 180^\circ\text{.}\)

Step 7 ：\(\text{Final Answer:}\)

Step 8 ：\(\boxed{\text{a) }\theta \approx 155^\circ}\)

Step 9 ：\(\boxed{\text{b) }\theta \approx 71^\circ}\)

Step 10 ：\(\boxed{\text{c) }\theta \approx 125^\circ}\)

Step 11 ：\(\boxed{\text{d) }\theta \approx 39^\circ}\)

Step 12 ：\(\boxed{\text{e) }\theta \approx 117^\circ}\)

Step 13 ：\(\boxed{\text{f) }\theta \approx 131^\circ}\)