SaiBook.us SAT-2

Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: Trigonometry Identities (quotient , co-function)

Grade: 10-a Lesson: S3-L4

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	Prove the identity \$ 1/tanθ - 1/(tan2θ) = 1/(sin2θ)\$.	A) Intifinty B) 0 C) Proved D) Not proved
2	Prove the identity \$ tanθ - cotθ = (2cos2θ)/(sin2θ)\$.	A) Proved B) Intifinty C) 0 D) Not proved
3	What is \$ sec( (5pi) /6 ) \$ by using cofunction?	A) -2 B) \$ - 2/\sqrt3 \$ C) \$ 1/2 \$ D) \$ - \sqrt3/2 \$
4	If \$ csc(pi/3 - θ ) = sec(pi/3) \$, what is the value of θ?(0 < θ < \$pi/2\$ ).	A) \$ pi/6\$ B) \$ (2pi)/3\$ C) \$ pi/3\$ D) \$ pi/2\$
5	Find the value of θ if \$cot θ = tan (θ/2 + π/12)\$ using cofunction identities.	A) \$ (5pi)/18 \$ B) \$ (5pi)/36 \$ C) \$ (5pi)/12\$ D) \$ pi/36 \$
6	Prove the identity \$ tan(-θ) + 1/(tan(-θ)) = - 2/(sin2θ)\$.	A) Proved B) Not proved C) 0 D) Intifinty
7	If \$ cotθ = - 2\$ and \$ sinθ = 3/\sqrt2 \$, what is the value of cosθ?	A) \$ - \sqrt2 \$ B) \$ - 3\sqrt2 \$ C) \$ 2/\sqrt2 \$ D) \$ \sqrt3/2 \$
8	Use cofunction identities to simplify the expression \$ cot(pi/2 - x) cscx \$.	A) cotx B) cosx C) secx D) cscx
9	If \$ sin( π/2−x) + cos (π/2−x) = 2\$, what is the value of sin2x?	A) 1 B) 4 C) 3 D) 2
10	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) \$ 112/5\$ C) \$ 193/20\$ D) \$ 139/20 \$

Problem Id

Problem

Options

Prove the identity \$ 1/tanθ - 1/(tan2θ) = 1/(sin2θ)\$.

A) Intifinty

B) 0

C) Proved

D) Not proved

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

A) Proved

B) Intifinty

C) 0

D) Not proved

What is \$ sec( (5pi) /6 ) \$ by using cofunction?

A) -2

B) \$ - 2/\sqrt3 \$

C) \$ 1/2 \$

D) \$ - \sqrt3/2 \$

If \$ csc(pi/3 - θ ) = sec(pi/3) \$, what is the value of θ?(0 < θ < \$pi/2\$ ).

A) \$ pi/6\$

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

C) \$ pi/3\$

D) \$ pi/2\$

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

A) \$ (5pi)/18 \$

B) \$ (5pi)/36 \$

C) \$ (5pi)/12\$

D) \$ pi/36 \$

Prove the identity \$ tan(-θ) + 1/(tan(-θ)) = - 2/(sin2θ)\$.

A) Proved

B) Not proved

C) 0

D) Intifinty

If \$ cotθ = - 2\$ and \$ sinθ = 3/\sqrt2 \$, what is the value of cosθ?

A) \$ - \sqrt2 \$

B) \$ - 3\sqrt2 \$

C) \$ 2/\sqrt2 \$

D) \$ \sqrt3/2 \$

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

A) cotx

B) cosx

C) secx

D) cscx

If \$ sin( π/2−x) + cos (π/2−x) = 2\$, what is the value of sin2x?

A) 1

B) 4

C) 3

D) 2

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) \$ 112/5\$

C) \$ 193/20\$

D) \$ 139/20 \$