math_trig_test_question_1$Math\phantom{\rule{0.22em}{0ex}}test\phantom{\rule{0.22em}{0ex}}Paper\phantom{\rule{0.22em}{0ex}}-1$Trigonometry
 Questions Marks Score Q-1Find the principal solutions of cotx=3$\phantom{\rule{0.22em}{0ex}}cotx=\sqrt{3}$ 2 Q-2Find the general solutions of Find general solution of cos 3x= cos 2x$Find\phantom{\rule{0.22em}{0ex}}general\phantom{\rule{0.22em}{0ex}}solution\phantom{\rule{0.22em}{0ex}}of\phantom{\rule{3.3em}{0ex}}cos\phantom{\rule{0.22em}{0ex}}3x=\phantom{\rule{0.22em}{0ex}}cos\phantom{\rule{0.22em}{0ex}}2x$ 2 Q-3Find the general solutions of sin x+sin 3x+sin 5x=0$\phantom{\rule{1.32em}{0ex}}sin\phantom{\rule{0.22em}{0ex}}x+sin\phantom{\rule{0.22em}{0ex}}3x+sin\phantom{\rule{0.22em}{0ex}}5x=0$ 2 Q-4Find the general solutions of cos x-sin x=-1$\phantom{\rule{0.44em}{0ex}}cos\phantom{\rule{0.22em}{0ex}}x-sin\phantom{\rule{0.22em}{0ex}}x=-1$ 2 Q-5aFind the cartesian co-ordinates of point, whose polar coordinates are (2,π2)$\begin{array}{l}Find\phantom{\rule{0.22em}{0ex}}the\phantom{\rule{0.22em}{0ex}}cartesian\phantom{\rule{0.22em}{0ex}}co-ordinates\phantom{\rule{0.22em}{0ex}}of\phantom{\rule{0.22em}{0ex}}point,\phantom{\rule{0.22em}{0ex}}whose\phantom{\rule{0.22em}{0ex}}polar\phantom{\rule{0.22em}{0ex}}\\ coordinates\phantom{\rule{0.22em}{0ex}}are\phantom{\rule{0.22em}{0ex}}\left(2,\frac{\pi }{2}\right)\end{array}$ 2 Q-6 aFind the polar co-ordinates of point, whose cartesian coordinates are (1,3)$\begin{array}{l}Find\phantom{\rule{0.22em}{0ex}}the\phantom{\rule{0.22em}{0ex}}polar\phantom{\rule{0.22em}{0ex}}co-ordinates\phantom{\rule{0.22em}{0ex}}of\phantom{\rule{0.22em}{0ex}}point,\phantom{\rule{0.22em}{0ex}}whose\phantom{\rule{0.22em}{0ex}}\\ cartesian\phantom{\rule{0.22em}{0ex}}coordinates\phantom{\rule{0.22em}{0ex}}are\phantom{\rule{0.22em}{0ex}}\left(1,\sqrt{3}\right)\end{array}$ 2 Q-7 Find the general solutions of sin x =tan x$sin\phantom{\rule{0.22em}{0ex}}x\phantom{\rule{0.22em}{0ex}}=tan\phantom{\rule{0.22em}{0ex}}x$ 2 Q-8 Find the general solutions of sin 𝜃=sin 𝛼$sin\phantom{\rule{0.22em}{0ex}}𝜃=sin\phantom{\rule{0.22em}{0ex}}𝛼$ 3 Q-9 Find the general solutions of cos 𝜃=cos 𝛼$\phantom{\rule{0.22em}{0ex}}cos\phantom{\rule{0.22em}{0ex}}𝜃=cos\phantom{\rule{0.22em}{0ex}}𝛼$ 3 Q-10 Find the general solutions of tan 𝜃=tan 𝛼$\phantom{\rule{0.22em}{0ex}}tan\phantom{\rule{0.22em}{0ex}}𝜃=tan\phantom{\rule{0.22em}{0ex}}𝛼$ 3 Q-11Prove that sin2𝜃=sin2𝛼 implies 𝜃=n𝜋±𝛼$Prove\phantom{\rule{0.22em}{0ex}}that\phantom{\rule{0.88em}{0ex}}si{n}^{2}𝜃=si{n}^{2}𝛼\phantom{\rule{1.1em}{0ex}}implies\phantom{\rule{1.1em}{0ex}}𝜃=n𝜋±𝛼$ 3 Q12Prove that cos2𝜃=cos2𝛼 implies 𝜃=n𝜋±𝛼$Prove\phantom{\rule{0.22em}{0ex}}that\phantom{\rule{0.88em}{0ex}}co{s}^{2}𝜃=co{s}^{2}𝛼\phantom{\rule{1.1em}{0ex}}implies\phantom{\rule{1.1em}{0ex}}𝜃=n𝜋±𝛼$ 3 Q13Prove that tan2𝜃=tan2𝛼 implies 𝜃=n𝜋±𝛼 $Prove\phantom{\rule{0.22em}{0ex}}that\phantom{\rule{0.88em}{0ex}}ta{n}^{2}𝜃=ta{n}^{2}𝛼\phantom{\rule{1.1em}{0ex}}implies\phantom{\rule{1.1em}{0ex}}𝜃=n𝜋±𝛼\phantom{\rule{0.22em}{0ex}}$ 3
$\begin{array}{l}Answer-1\phantom{\rule{0.22em}{0ex}}:\phantom{\rule{0.88em}{0ex}}\frac{5𝜋}{6},\phantom{\rule{0.22em}{0ex}}\frac{11𝜋}{6}\\ \\ Answer-2\phantom{\rule{0.22em}{0ex}}:\phantom{\rule{0.88em}{0ex}}x=\frac{2n𝜋}{5}\phantom{\rule{0.66em}{0ex}}or\phantom{\rule{0.22em}{0ex}}x=2m𝜋\\ \\ Answer-3\phantom{\rule{0.22em}{0ex}}:\phantom{\rule{0.88em}{0ex}}x=\frac{n𝜋}{3},\phantom{\rule{0.22em}{0ex}}x=m𝜋±\frac{𝜋}{3}\\ \\ Answer-4\phantom{\rule{0.22em}{0ex}}:\phantom{\rule{0.88em}{0ex}}x=2n𝜋+\frac{𝜋}{2},\phantom{\rule{0.22em}{0ex}}x=2n𝜋-\pi \\ \\ Answer-5\phantom{\rule{0.22em}{0ex}}:\phantom{\rule{0.66em}{0ex}}\left(\sqrt{2}\phantom{\rule{0.44em}{0ex}},\phantom{\rule{0.22em}{0ex}}\sqrt{2}\right)\\ \\ Answer-6\phantom{\rule{0.22em}{0ex}}:\phantom{\rule{0.66em}{0ex}}\left(2\phantom{\rule{0.22em}{0ex}},\phantom{\rule{0.22em}{0ex}}\frac{𝜋}{3}\right)\\ \\ Answer-7\phantom{\rule{0.22em}{0ex}}:\phantom{\rule{0.88em}{0ex}}x=n𝜋\phantom{\rule{0.66em}{0ex}}or\phantom{\rule{0.44em}{0ex}}x=2m𝜋\\ \\ Answer-8\phantom{\rule{0.22em}{0ex}}:\phantom{\rule{0.44em}{0ex}}𝜃=n𝜋+\left(-1{\right)}^{n}𝛼\\ \phantom{\rule{0.44em}{0ex}}\\ Answer-9\phantom{\rule{0.22em}{0ex}}:\phantom{\rule{0.66em}{0ex}}𝜃=2n𝜋±𝛼\\ \\ Answer-10\phantom{\rule{0.22em}{0ex}}:\phantom{\rule{0.44em}{0ex}}𝜃=n𝜋+𝛼\\ \end{array}$