Math 115 Carter Sample Test 3
1. Simplify sin(A+B)−sin(A−B).
2. Use the facts that sin ( π
12 )=√2−√3
2and cos ( π
12 )=√2+√3
2to determine the values of
the six trigonometric functions at the angle 5π
12 .
3. Verify the identity: 1−cos x
sin x=sin x
1 + cos x
Hint: Use the Pythagorean Theorem.
4. Verify the identity: sin x+ cos x
sec x+ csc x=sin x
sec x
5. Compute the exact value of Arccot(−√3) as an angle in radians.
6. Evaluate arcsin(cos ( 5π
6))
7. Use the graphing capablilities of your calculator to approximate the solutions (that are
in the interval [0,2π]) to the equation:
xcos x−2=0
8. Find all solutions for 0 ≤x<2π,
3 sin2x= 3sin x+2
9. Solve the triangle, if possible: A= 131◦;C=23
◦;b=10
10. Solve the triangle, if possible: C=28
◦430;a=6M;b=9M
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