a)


b)
Genaral solutions


Suppose sin 0 - 5 and 0<o<". Determine sin(20). DO NOT use a calculator
Solve sin(20) NIE for 0 <o<2m. Give your answer in radians.
3 Given sin osesan and sin B -7 37 25 <B< 27. Find cos(0 + B).
= Let cos(6) sin(0) B - sin() cos() and 0 << 27 (i) Calculate the eigenvalues of B. Hence prove that the modulus of the eigenvalues is equal to one. (ii) Calculate the eigenvectors of B.
Solve sin’(x) + sin(x) = 0 for 0 SI<2m. Give your answer in radians.
State the quadrant in which lies. sin(8) <0, cos(8) < 0 OII III OIV 8 If sin() and 8 is in the 1st quadrant, find the exact value for cos(8). 9 cos(8) - > Next Question State the quadrant in which lies. tan(8) > 0, csc(8) < 0 01 OII O III OIV
ſi, if 0 St<T, y" + 4y = 10, if a St< 0. y(0) = 0, y(0) = 0. 9
12. (8 points) Solve (sin 0)2 = 5.0 5 0 < 2t.
T Find the length of the curve e' cos(t) e' sin(t) for 0 < t < 2 y (Hint: You can simplify the integrand by expanding the argument inside the square root and applying the Pythagorean identity, sinº (0) + cos²O) = 1.)
Solve fort, 0 < t < 27. 32 sin(t)cos(t) = 12 sin(t)