Tag: trigonometry

Quizzes (11) Questions (86)

Questions Related to trigonometry

Multiple choice using trigonometric tables trigonometric ratios of some specific angles trigonometric identities trigonometry maths

$\tan 5\tan 25\tan 30\tan 65 \tan 85$ is equal to

  1. $3$
  2. $\surd {3}$
  3. $1$
  4. $\dfrac {1}{\surd {3}}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using complementary angle properties, tan(85) = cot(5) = 1/tan(5) and tan(65) = cot(25) = 1/tan(25). Thus, tan(5) and tan(85) cancel out, as do tan(25) and tan(65). We are left with tan(30 degrees), which equals 1 / sqrt(3).

Multiple choice using trigonometric tables trigonometric ratios of some specific angles trigonometric identities trigonometry maths

$\tan 20 ^ { \circ } + \tan 40 ^ { \circ } + \sqrt { 3 } \tan 20 ^ { \circ } \tan 40 ^ { \circ }$  is equal to

  1. $\dfrac { \sqrt { 3 } } { 2 }$
  2. $\dfrac { \sqrt { 3 } } { 4 }$
  3. $\sqrt { 3 }$
  4. $1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From the identity tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B)), let A = 20 degrees and B = 40 degrees, so tan(60 degrees) = sqrt(3) = (tan(20) + tan(40)) / (1 - tan(20)tan(40)). Cross-multiplying gives tan(20) + tan(40) = sqrt(3) - sqrt(3)tan(20)tan(40), which rearranges to tan(20) + tan(40) + sqrt(3)tan(20)tan(40) = sqrt(3).

Multiple choice using trigonometric tables trigonometric ratios of some specific angles trigonometric identities trigonometry maths

If $\alpha =685^o$, then $(\cos\alpha -\sin\alpha)$ is equivalent to?

  1. $-\cos 35^o-\sin 35^o$
  2. $-\cos 35^o +\sin 35^o$
  3. $\cos 35^o-\sin 35^o$
  4. $\cos 35^o+\sin 35^o$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Reduce alpha = 685 degrees modulo 360 degrees: 685 - 2*360 = 685 - 720 = -35 degrees. Then cos(-35 degrees) - sin(-35 degrees) = cos(35 degrees) + sin(35 degrees) since cosine is even and sine is odd.

Multiple choice using trigonometric tables trigonometric ratios of some specific angles trigonometric identities trigonometry maths

The distance between $A ( \cos \theta , \sin \theta )$ and $B ( - \sin \theta , \cos \theta )$ is

  1. 1
  2. $2 + 2 \sin \theta$
  3. $1 + \sin \theta$
  4. $\sqrt { 2 }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given $A(\cos \theta,\sin \theta)$ and $B(-\sin \theta,\cos \theta)$

Distance between $AB=\sqrt{(\cos \theta+\sin \theta)^2+(\sin \theta-\cos \theta)^2}=\sqrt{\cos^2 \theta+\sin ^2 \theta+2\sin \theta\cos \theta+\cos^2\theta+\sin ^2 \theta-2\sin \theta\cos \theta}=\sqrt{1+1}=\sqrt{2}$

Multiple choice using trigonometric tables trigonometric ratios of some specific angles trigonometric identities trigonometry maths

$\displaystyle3\tan^2{30^\circ}+\frac{4}{3}\cos^2{30^\circ}-2\sin^2{45^\circ}-\frac{1}{3}\sin^2{60^\circ}$ is equal to__________________.

  1. $\displaystyle\frac{1}{4}$
  2. $\displaystyle\frac{3}{4}$
  3. $1$
  4. $0$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given 


$3\tan ^230+\dfrac 43\cos ^230-2\sin ^245-\dfrac 13\sin ^260$

$=3\left(\dfrac 1{\sqrt 3}\right)^2+\dfrac 43\left(\dfrac {\sqrt 3}2 \right)^2-2\left(\dfrac 1{\sqrt 2}\right)^2-\dfrac 13\left(\dfrac {\sqrt 3}2\right)^2$

$=1+1-1-\dfrac 14$

$= \dfrac 34$