SaiBook.us SAT-3

Lesson Example Discussion Quiz: Class Homework

Quiz In Class

Title: Trignometry

Grade: Core-SAT3 Lesson: S7-P1

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: in Class

Problem Id	Problem	Options
1	If tan(α) = \$5/12\$ and sin(β) = \$3/5\$, where α and β are acute angles, calculate the value of tan(α-β).	A) \$16/63\$ B) \$-16/63\$ C) \$-12/5\$ D) \$12/5\$
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) \$ 12/13\$ and \$ 5/13\$ C) \$ - 5/13\$ and \$ 12/13\$ D) \$ - 12/13\$ and \$ - 5/13\$
3	Consider △ACB, right angled at C, in which AC = 20 units, BC = 21 units ∠ABC = \theta. Determine the value of \$cos^2 \theta + sin^2 \theta\$ and \$cos^2 \theta - sin^2 \theta\$. $6$	A) 1 and \$41/841\$ B) 0 and \$41/841\$ C) 1 and \$29/20\$ D) 0 and \$841/29\$
4	Given \$sinA = 4/5 \$, find the other trigonometric ratios of the angle A. $4$	A) \$tan A = 4/3, cosA = 3/4, cscA = 5/4, secA = 4/3, cotA = 3/4 \$ B) \$tanA = - 4/3, cosA = - 3/5, cscA = 4/5, secA = 5/3, cotA = - 3/4 \$ C) \$tanA = 5/4, cosA = 5/3, cscA= 4/5, secA = 5/3, cotA= 4/3 \$ D) \$tanA = 4/3, cosA = 3/5, cscA = 5/4, secA = 5/3, cotA = 3/4 \$
5	Simplify the expression \$(sin^2(-\theta) - cos^2(\theta)) / (sin(-\theta) - cos(-\theta))\$.	A) \$csc\theta - sec\theta\$ B) \$cos\theta + sin\theta\$ C) \$cos\theta - sin\theta\$ D) \$csc\theta + sec\theta\$
6	Find the value of θ if \$cosθ = sin (θ/2 + (3π)/12)\$ using cofunction identities.	A) \$ pi/3 \$ B) \$ pi/4 \$ C) \$ pi/2 \$ D) \$ pi/6 \$
7	If \$cos(θ) = -1/2\$ and θ is in the third quadrant, find the values of sin(θ) and tan(θ).	A) \$sin\theta = \sqrt(3)/2\$ and \$tan\theta = - \sqrt(3)\$ B) \$sin\theta = - \sqrt(3)/2\$ and \$tan\theta = \sqrt(3)\$ C) \$sin\theta = \sqrt(3)/2\$ and \$tan\theta = \sqrt(3)\$ D) \$sin\theta = -\sqrt(3)/2\$ and \$tan\theta = - \sqrt(3)\$
8	If sin \$ \theta = -7/8 \$and \$ \theta \$ is in Quadrant III, find the values of tan(\$ \theta \$) and cos(\$ \theta \$).	A) \$(7\sqrt(15))/15\$, \$- \sqrt(15)/8\$ B) \$- (7\sqrt(15))/15\$ , \$\sqrt(8)/15\$ C) \$\sqrt(8)/15\$ , \$\sqrt(- 7)/15\$ D) \$\sqrt(- 15)/8\$ , \$- (7\sqrt(15))/15\$
9	Simplify the expression: \$ ((1+ sec(\theta)) / (sin(\theta))) + ((1 - csc(\theta))/cos(\theta)) \$.	A) \$sin(\theta) + csc(\theta)\$ B) \$sin(\theta) + cos(\theta)\$ C) \$sec(\theta) + cos(\theta)\$ D) \$sec(\theta) + csc(\theta)\$
10	Consider △ACB, right-angled at C, in which AB = 31 units, BC = 22 units, and ∠ABC = \$ \theta \$ (see fig). Determine the values of \$ sin^2 \theta - cos^2 \theta \$. $8$	A) \$49/41\$ B) \$961/7\$ C) \$7/961\$ D) \$41/49\$

Problem Id

Problem

Options

If tan(α) = \$5/12\$ and sin(β) = \$3/5\$, where α and β are acute angles, calculate the value of tan(α-β).

A) \$16/63\$

B) \$-16/63\$

C) \$-12/5\$

D) \$12/5\$

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

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

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

Consider △ACB, right angled at C, in which AC = 20 units, BC = 21 units ∠ABC = \theta. Determine the value of \$cos^2 \theta + sin^2 \theta\$ and \$cos^2 \theta - sin^2 \theta\$.

$6$

A) 1 and \$41/841\$

B) 0 and \$41/841\$

C) 1 and \$29/20\$

D) 0 and \$841/29\$

Given \$sinA = 4/5 \$, find the other trigonometric ratios of the angle A.

$4$

A) \$tan A = 4/3, cosA = 3/4, cscA = 5/4, secA = 4/3, cotA = 3/4 \$

B) \$tanA = - 4/3, cosA = - 3/5, cscA = 4/5, secA = 5/3, cotA = - 3/4 \$

C) \$tanA = 5/4, cosA = 5/3, cscA= 4/5, secA = 5/3, cotA= 4/3 \$

D) \$tanA = 4/3, cosA = 3/5, cscA = 5/4, secA = 5/3, cotA = 3/4 \$

Simplify the expression \$(sin^2(-\theta) - cos^2(\theta)) / (sin(-\theta) - cos(-\theta))\$.

A) \$csc\theta - sec\theta\$

B) \$cos\theta + sin\theta\$

C) \$cos\theta - sin\theta\$

D) \$csc\theta + sec\theta\$

Find the value of θ if \$cosθ = sin (θ/2 + (3π)/12)\$ using cofunction identities.

A) \$ pi/3 \$

B) \$ pi/4 \$

C) \$ pi/2 \$

D) \$ pi/6 \$

If \$cos(θ) = -1/2\$ and θ is in the third quadrant, find the values of sin(θ) and tan(θ).

A) \$sin\theta = \sqrt(3)/2\$ and \$tan\theta = - \sqrt(3)\$

B) \$sin\theta = - \sqrt(3)/2\$ and \$tan\theta = \sqrt(3)\$

C) \$sin\theta = \sqrt(3)/2\$ and \$tan\theta = \sqrt(3)\$

D) \$sin\theta = -\sqrt(3)/2\$ and \$tan\theta = - \sqrt(3)\$

If sin \$ \theta = -7/8 \$and \$ \theta \$ is in Quadrant III, find the values of tan(\$ \theta \$) and cos(\$ \theta \$).

A) \$(7\sqrt(15))/15\$, \$- \sqrt(15)/8\$

B) \$- (7\sqrt(15))/15\$ , \$\sqrt(8)/15\$

C) \$\sqrt(8)/15\$ , \$\sqrt(- 7)/15\$

D) \$\sqrt(- 15)/8\$ , \$- (7\sqrt(15))/15\$

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

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

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

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

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

Consider △ACB, right-angled at C, in which AB = 31 units, BC = 22 units, and ∠ABC = \$ \theta \$ (see fig). Determine the values of \$ sin^2 \theta - cos^2 \theta \$.

$8$

A) \$49/41\$

B) \$961/7\$

C) \$7/961\$

D) \$41/49\$