SaiBook.us SAT-3

Quiz At Home

Title: Algebra, Trignometry

Grade: Core-SAT3 Lesson: Sfirst-F3

Explanation: Hello Students, time to practice and review. Let us take next 10-15 minutes to solve the ten problems using the Quiz Sheet. Then submit the quiz to get the score. This is a good exercise to check your understanding of the concepts.

Quiz: at Home

Problem Id	Problem	Options
1	Simplify the expression: \$ ((1+ sec(\theta)) / (sin(\theta))) + ((1 - csc(\theta))/cos(\theta)) \$.	A) \$(sec(\theta) + csc(\theta))\$ B) \$(sec(\theta) + cos(\theta))\$ C) \$(sin(\theta) + cos(\theta))\$ D) \$(sin(\theta) + csc(\theta))\$
2	In a circle with a center O, points A and B are on the circle. If the arc \$\overset{\frown}{AB}\$ measures \$(13π)/15\$ radians, what is the measure of the central angle ∠AOB in degrees?	A) 138 B) 156 C) 215 D) 181
3	In the given figure, PO: OQ = 6:8 and perimeter of △POQ = 96 m. Determine OP, QR, and QP. $1$	A) OP = 40 m , RQ = 64 m and QP = 24 m B) OP = 64 m , RQ = 24 m and QP = 40 m C) OP = 40 m , PQ = 24 m and QP = 64 m D) OP = 24 m , RQ = 64 m and QP = 40 m
4	Solve the equation \$cot(θ/2) * (1 - cos(θ)) = \sqrt2/2 \$, 0° ≤ θ < 180°.	A) \$ pi/3, (4pi)/3 \$ B) \$ 0, 2pi \$ C) \$ pi/4, (3pi)/4 \$ D) \$ pi/2, (3pi)/2 \$
5	If tan \$ \theta = -5/12 \$and \$ \theta \$ is in Quadrant IV, find the values of sin(\$ \theta \$) and cos(\$ \theta \$).	A) \$ 5/13\$ and \$ - 12/13\$ B) \$ - 5/13\$ and \$ 12/13\$ C) \$ 12/13\$ and \$ 5/13\$ D) \$ - 12/13\$ and \$ - 5/13\$
6	If \$ sin^(-1)(x) + sin^(-1)(y) + sin^(-1)(z) = (3pi)/2 \$, then calculate the value of x + y?	A) 5 B) 1 C) 2 D) 6
7	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) \$ 193/20 \$ C) \$ 112/5\$ D) \$ 139/20\$
8	Find the value of the expression using a reciprocal identity. \$sin\theta = - 1/2\$ and \$tan\theta = \sqrt(3)/3\$ , \$cos\theta\$.	A) \$-\sqrt(3)/2\$ B) \$\sqrt(2)/3\$ C) \$\sqrt(3)/2\$ D) \$-\sqrt(2)/3\$
9	Solve triangle UVW, given u = 10, v = 20, and w = 30. Find the angle U, V and W?	A) A = 180°, B = 180° and C = 180° B) A = 0°, B = 360° and C = 180° C) A = 0°, B = 0° and C = 180° D) A = 0°, B = 10° and C = 180°
10	Triangle DEF has side DE measuring 6 cm, side EF measuring 9 cm, and the angle between sides DE and EF measures 60 degrees. Find the length of side DF.	A) \$ \sqrt63 \$ B) \$ \sqrt78 \$ C) \$ \sqrt73 \$ D) \$ \sqrt68 \$

Problem Id

Problem

Options

Simplify the expression: \$ ((1+ sec(\theta)) / (sin(\theta))) + ((1 - csc(\theta))/cos(\theta)) \$.

A) \$(sec(\theta) + csc(\theta))\$

B) \$(sec(\theta) + cos(\theta))\$

C) \$(sin(\theta) + cos(\theta))\$

D) \$(sin(\theta) + csc(\theta))\$

In a circle with a center O, points A and B are on the circle. If the arc \$\overset{\frown}{AB}\$ measures \$(13π)/15\$ radians, what is the measure of the central angle ∠AOB in degrees?

A) 138

B) 156

C) 215

D) 181

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

$1$

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

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

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

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

Solve the equation \$cot(θ/2) * (1 - cos(θ)) = \sqrt2/2 \$, 0° ≤ θ < 180°.

A) \$ pi/3, (4pi)/3 \$

B) \$ 0, 2pi \$

C) \$ pi/4, (3pi)/4 \$

D) \$ pi/2, (3pi)/2 \$

If tan \$ \theta = -5/12 \$and \$ \theta \$ is in Quadrant IV, find the values of sin(\$ \theta \$) and cos(\$ \theta \$).

A) \$ 5/13\$ and \$ - 12/13\$

B) \$ - 5/13\$ and \$ 12/13\$

C) \$ 12/13\$ and \$ 5/13\$

D) \$ - 12/13\$ and \$ - 5/13\$

If \$ sin^(-1)(x) + sin^(-1)(y) + sin^(-1)(z) = (3pi)/2 \$, then calculate the value of x + y?

A) 5

B) 1

C) 2

D) 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) \$ 193/20 \$

C) \$ 112/5\$

D) \$ 139/20\$

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

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

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

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

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

Solve triangle UVW, given u = 10, v = 20, and w = 30. Find the angle U, V and W?

A) A = 180°, B = 180° and C = 180°

B) A = 0°, B = 360° and C = 180°

C) A = 0°, B = 0° and C = 180°

D) A = 0°, B = 10° and C = 180°

Triangle DEF has side DE measuring 6 cm, side EF measuring 9 cm, and the angle between sides DE and EF measures 60 degrees. Find the length of side DF.

A) \$ \sqrt63 \$

B) \$ \sqrt78 \$

C) \$ \sqrt73 \$

D) \$ \sqrt68 \$