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Definitions: FSc Part1 KPK
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measure of the angle, gives the same value of the function. * **Circular system (Radians):** A radia... $16^\circ 13' 9''$ * **Period of Trigonometric Function:** The smallest +ve number which when added ... ular measurement of the angle gives same value of function is called period. \\ e.g. $sin(\alpha+2\pi)=... he equation, containing at least one trigonometry function are called Trigonometry equation. \\ e.g. $s
Question 1, Exercise 10.1 @math-11-kpk:sol:unit10
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==== Question 1(i) ===== Write as a trigonometric function of a single angle. $\sin {{37}^{\circ }}\cos... === Question 1(ii)===== Write as a trigonometric function of a single angle. $\cos {{83}^{\circ }}\cos... == Question 1(iii)===== Write as a trigonometric function of a single angle. $\cos {{19}^{\circ }}\cos... === Question 1(iv)===== Write as a trigonometric function of a single angle. $\sin {{40}^{\circ }}\cos
Unit 03: Vectors (Solutions) @math-11-kpk:sol
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epresentation of a vector. * Give the following fundamental definitions using geometrical representat... present a vector in a Cartesian plane by defining fundamental unit vectors $i$ and $j$. * Recognize a... r. * Find magnitude of a vector. * Repeat all fundamental definitions for vectors in space which, i
Question 7 and 8 Exercise 6.2 @math-11-kpk:sol:unit06
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_2=5$ ways $E_3$ occurs in $m_3=5$ ways Thus by fundamental principle of counting the total number of... 2=4$ ways $E_3$ occurs in $m_3=3$ ways. Thus by fundamental principle of 'counting the total number o... ts not vowel can be arrange are $=3$ ! Hence, by fundamental principle of counting the total number of
Unit 10: Trigonometric Identities of Sum and Difference of Angles (Solutions) @math-11-kpk:sol
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will be able to * Define allied angles * Use fundamental law and its deductions to derive trigonom... ngle, half angle and triple angle identities from fundamental law and its deductions. * Express the p
Question 3 and 4 Exercise 6.2 @math-11-kpk:sol:unit06
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awar, Pakistan. =====Question 3(i)===== Prove by Fundamental principle of counting $^n P_r=n(^{n-1} P_... P_r\end{align} =====Question 3(ii)===== Prove by Fundamental principle of counting $^n P_r=^{n-1} P_r+
Question 11 Exercise 6.2 @math-11-kpk:sol:unit06
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2$ occurs in $m_2=5$. Hence the total numbers by fundamental principle of counting greater than $10$ a... it digit:Event $E_3$ occurs in $m_3=4$. Hence by fundamental principle of counting numbers greater tha
Unit 06: Permutation, Combination and Probability (Solutions) @math-11-kpk:sol
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rst $n$ natural numbers by $n!$ * Recognize the fundamental principle of counting and illustrate this
Question 5 and 6 Exercise 6.2 @math-11-kpk:sol:unit06
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Ten Thousand: $E_4$ occurs in $m_4=1$. Thus by fundamental principle of counting the total number of
Question 9 Exercise 6.3 @math-11-kpk:sol:unit06
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at four women to be selected are ${ }^6 C_4$. By fundamental principle of counting the total number of
Question 7 & 8 Review Exercise 6 @math-11-kpk:sol:unit06
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_4$ occurs with $m_4=4$ different ways. Thus by fundamental principle of multiplication, the total
Question 9 & 10 Review Exercise 6 @math-11-kpk:sol:unit06
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of ways that $2$ men can sit are: $2 !$ Thus by fundamental principle of counting the total number of
Question 8 and 9, Exercise 10.2 @math-11-kpk:sol:unit10
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ta $ in term of first power of one or more cosine functions. ====Solution==== \begin{align}{{\cos}^{4}}