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

In the given figure, PO: OQ = 6:8 and perimeter of △POQ = 96 m. Determine OP, QR, and QP.

A) OP = 24 m , RQ = 64 m and QP = 40 m

B) OP = 40 m , PQ = 24 m and QP = 64 m

C) OP = 40 m , RQ = 64 m and QP = 24 m

D) OP = 64 m , RQ = 24 m and QP = 40 m

Find the value of the expression using a reciprocal identity. \$sin\theta = -1/2\$ and \$tan\theta = \sqrt(3)/3\$ , \$cos\theta\$.

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

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

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

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

Prove the identity \$ tanθ - cotθ = (2cos2θ)/(sin2θ)\$.

A) Proved

B) Not proved

C) Intifinty

D) 0

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

A) 0

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

C) 1

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

Triangle XYZ is a right triangle with a right angle at Y. XZ (hypotenuse) has a length of 10 cm and XY is 6 cm. A circle is drawn with T as the center and TY as the radius. What is the length of the chord of this circle passing through Y and Z?

A) 7

B) 8

C) 9

D) 10

Evaluate \$ (cscx + cotx) (( 1 - cosx)/sinx ) \$.

A) \$ sinx/cosx \$

B) \$ 1/sinx \$

C) 1

D) \$ 1/cosx \$

Use cofunction identities to simplify the expression \$ cot(pi/2 - x) cscx \$.

A) cscx

B) cosx

C) cotx

D) secx

Triangle PQR is a right triangle with a 90-degree angle at vertex Q. The length of side PQ is 25 and the length of the side QR is 60. Triangle STU is similar to triangle PQR. The vertices S, T, and U correspond to vertices P, Q, and R, respectively. What is the value of cos∠U?

A) \$5/13\$

B) \$13/12\$

C) \$5/12\$

D) \$5/6\$

Use cofunction identities to find the value of \$sin(180° - x) - tan(360° - x) - 7(sin270° - x)\$ given \$ sinx = 3/5 \$, where 0° < x < 90°.

A) \$ - 23/4\$

B) \$ 139/20\$

C) \$ 112/5\$

D) \$ 193/20 \$