Math 9th Chap 6 : Topic 4 - Maryam Publications

Math Chapter 6 : Topic 4

Trig Identities

1 / 25

If $sin \theta=$ $\frac{3}{5} $, then $cos \theta$ is:

A) $\frac{2}{5}$

B) $\frac{4}{5}$

C) $\frac{5}{4}$

D) $\frac{3}{4}$

2 / 25

Which identity is always true?

A) $sin \theta+cos \theta=1$

B) $tan \theta=1$

C) $sin \theta=cos \theta$

D) $tan \theta=$ $\frac{sin \theta}{cos \theta}$

3 / 25

If $tan \theta=$ $\frac{5}{12} $, then $sin \theta$ is:

A) $\frac{13}{5}$

B) $\frac{5}{13}$

C) $\frac{12}{5}$

D) $\frac{12}{13}$

4 / 25

Simplify: $\frac{sin \theta}{cos \theta}$

A) $tan \theta$

B) $1$

C) $sec \theta$

D) $cot \theta$

5 / 25

Which expression equals 1?

A) $sin \theta-cos \theta$

B) $tan \theta+cot \theta$

C) ${tan}^{2} \theta$

D) ${sin}^{2} \theta+{cos}^{2} \theta$

6 / 25

If $cos \theta=$ $\frac{8}{17} $, then $sin \theta$ is:

A) $\frac{17}{15}$

B) $\frac{15}{17}$

C) $\frac{8}{15}$

D) $\frac{9}{17}$

7 / 25

Simplify: $\frac{1}{sin \theta}$

A) $cosec \theta$

B) $sec \theta$

C) $tan \theta$

D) $cot \theta$

8 / 25

If $tan \theta=1$, then $sin \theta=cos \theta$. This shows:

A) Identity

B) Function

C) Equation

D) Relation

9 / 25

Simplify: $\frac{{sin}^{2} \theta}{1 - {cos}^{2} \theta}$

A) $cos \theta$

B) $tan \theta$

C) $sin \theta$

D) $1$

10 / 25

If $sin \theta=$ $\frac{12}{13} $, then $tan \theta$ is:

A) $\frac{12}{5}$

B) $\frac{5}{12}$

C) $\frac{12}{13}$

D) $\frac{13}{12}$

11 / 25

Which identity is used to convert tangent into sine and cosine?

A) $tan \theta=$ $\frac{sin \theta}{cos \theta}$

B) $1+{tan}^{2} \theta={sec}^{2} \theta$

C) ${sin}^{2} \theta+{cos}^{2} \theta=1$

D) $cot \theta=1 / tan \theta$

12 / 25

Simplify: $\frac{1 - {cos}^{2} \theta}{{sin}^{2}\theta}$

A) ${tan}^{2} \theta$

B) ${cot}^{2} \theta$

C) ${sec}^{2} \theta$

D) $1$

13 / 25

If $sin \theta=cos \theta$, then $\theta$ is:

A) ${45}^{o}$

B) ${60}^{o}$

C) ${30}^{o}$

D) ${90}^{o}$

14 / 25

Simplify: $\frac{cos \theta}{sin \theta}$

A) $cosec \theta$

B) $sec \theta$

C) $cot \theta$

D) $tan \theta$

15 / 25

If $tan \theta=$ $\frac{3}{4} $, then $cos \theta$ is:

A) $\frac{3}{5}$

B) $\frac{5}{4}$

C) $\frac{4}{5}$

D) $\frac{5}{3}$

16 / 25

Which identity helps in proving ${sec}^{2} \theta-{tan}^{2} \theta=1$?

A) $tan=sin \theta / cos \theta$

B) $1+{tan}^{2} \theta= {sec}^{2} \theta$

C) ${sin}^{2} \theta+{cos}^{2} \theta=1$

D) $cot \theta=cos \theta / sin \theta$

17 / 25

Simplify: $\frac{1}{cos \theta}$

A) $tan \theta$

B) $cosec \theta$

C) $cot \theta$

D) $sec \theta$

18 / 25

If $cos \theta=$ $\frac{5}{13} $, then $tan \theta$ is:

A) $\frac{5}{12}$

B) $\frac{12}{5}$

C) $\frac{13}{5}$

D) $\frac{12}{13}$

19 / 25

Simplify: $\frac{tan \theta}{sec \theta}$

A) $tan \theta$

B) $cot \theta$

C) $cos \theta$

D) $sin \theta$

20 / 25

Which identity is used to eliminate sine in terms of cosine?

A) $sec \theta=1 / cos \theta$

B) ${sin}^{2} \theta+{cos}^{2} \theta=1$

C) $cot \theta=cos \theta / sin \theta$

D) $tan \theta=sin \theta / cos \theta$

21 / 25

If $tan \theta=1$, then $sec \theta$ is:

A) $\sqrt{3}$

B) $\sqrt{2}$

C) $1$

D) $2$

22 / 25

Simplify: $\frac{{sec}^{2} \theta - 1}{{tan}^{2} \theta}$

A) $cot \theta$

B) $tan \theta$

C) $1$

D) $sec \theta$

23 / 25

If $sin \theta=$ $\frac{8}{17} $, then $cos \theta$ is:

A) $\frac{8}{15}$

B) $\frac{9}{17}$

C) $\frac{15}{17}$

D) $\frac{17}{15}$

24 / 25

Simplify: $\frac{1}{tan \theta}$

A) $cos \theta$

B) $sin \theta$

C) $cot \theta$

D) $sec \theta$

25 / 25

Which identity proves $\frac{1}{sin \theta}$ $=csc \theta $?

A) Quotient

B) Product

C) Pythagorean

D) Reciprocal

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