Given that cos(α) = \$3/4\$ and tan(β) = \$5/12\$, where α and β are acute angles, find the value of sin(α + β).

A) \$9/16\$

B) \$4/3\$

C) \$16/9\$

D) \$3/5\$

If sin \$ \theta \$ = -0.6 and \$ \theta \$ is in Quadrant III, find the values of cos(\$ \theta \$) and tan(\$ \theta \$).

A) \$ - 0.8\$, \$ 0.75\$

B) \$ 0.75\$, \$ -0.8\$

C) \$ 0.8\$, \$ -0.75\$

D) \$ -0.75\$, \$ 0.8\$

Given tan α = -\$ \sqrt3\$ and cos α < 0, what is the value of sin(α)?

A) \$ \sqrt3/2 \$

B) \$ 1/2 \$

C) \$- 1/2 \$

D) \$ - \sqrt3 \$

What is the value of \$cos((5pi) / 4)\$.

A) 0

B) -1

C) 1

D) \$\sqrt(2)\$

Evaluate: \$ cos((7pi)/6) sin(pi/3) - sin((7pi)/6) cos(pi/3) \$.

A) \$ - \sqrt(3)/2\$

B) 1

C) \$ \sqrt(3)/2\$

D) -1

If \$cos(α)= 1/3\$ and α is in the second quadrant, find tan(α).

A) \$ - 2 \sqrt 2 \$

B) \$ \sqrt 2 \$

C) \$ 2 \sqrt 2 \$

D) \$ - \sqrt 2 \$

If tan(θ)= \$4/3\$ and θ is in the third quadrant, find the exact values of sin(2θ) and cos(2θ).

A) 24, - 31

B) 12, - 32

C) 24, - 42

D) - 18, - 23

If cos(α) = \$ 5/6 \$ and tan(β) = \$ 2/3 \$, find sin(α)cos(β).

A) \$(9 \sqrt 13) / (2 \sqrt 13) \$

B) \$ \sqrt 11 / (2 \sqrt 13) \$

C) \$ (13 \sqrt 22) / (2 \sqrt 53) \$

D) \$(19 \sqrt 13) / (2 \sqrt 13) \$

If tan(β)= \$− 2/7\$ and β is in Quadrant III, determine the values of sin(β) and cos(β).

A)\$ 7/\sqrt(53)\$, \$ - 2/\sqrt(53) \$

B) \$ 7/\sqrt(53)\$, \$ 2/\sqrt(53) \$

C)\$ -7/\sqrt(53)\$, \$ - 2/\sqrt(53) \$

D) \$ -7/\sqrt(53)\$, \$ 2/\sqrt(53) \$

Simplify \$ ( cos(pi/2) times csc((3pi)/4))/(sec(pi/4) - tan(pi/3)) \$.

A) \$ \sqrt 2/(\sqrt2 - \sqrt3) \$

B) \$ \sqrt 2/(\sqrt6) \$

C) 1

D) 0