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Mathematics Grade 10 Unit 4: Trigonometric Functions

national exam questions have come from this unit. It runs 52 pages; one careful study pass takes about 4.5 hours, and its difficulty is moderate among Mathematics units. Each section below lists the questions set from it, with the year, and opens the page that teaches it.

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4.1 Radian Measure of angle · read p. 200
  • 2014 E.C., Q2 – The radian measure of an angle of 120° is equal to:
4.2 Basic Trigonometric Function · read p. 207
  • 2018 E.C., Q34 – What is the fundamental period of the function $f(x)=\sin(x)$?
  • 2017 E.C., Q6 – Consider the graph of a certain trigonometric function given below. Which one of the following functions represents the above graph for $-\frac{\pi}{2} \leq x \leq \frac{5\pi}{2}$?
  • 2017 E.C., Q33 – Which of the following is true about the cosecant value of the given angles?
  • 2016 E.C., Q23 – For $0^\circ \le \theta \le 90^\circ$, which of the following relationships describes the co-relationship of angle $\theta$?
  • 2015 E.C., Q30 – Let $f(x)=-\frac{1}{3}\cos\left(2^{x^3}-\frac{\pi}{3}\right)+1$. Then what is the period and Phase shift of the graph of $f$ respectively?
  • 2015 E.C., Q39 – Which of the following functions has a graph that completes one full cycle on $\left[-\pi,\frac{11\pi}{4}\right]$?
  • 2015 E.C., Q39 – Which one of the following integrals of trigonometric functions is the true? (sin 2x)dx = ∫ cos 2x + 2 1 C 10(cos 10x)dx = ∫ −sin 10x + C
  • 2015 E.C., Q28 – Which one of the following limit values is correct for the limit of the given function?
  • 2015 E.C., Q36 – Which of the following is equal to $\int 3\cos 3x\,dx$?
  • 2015 E.C., Q4 – Which one of the following is true about the function $f(x)=\cos x$?
  • 2014 E.C., Q15 – Which one of the following gives the polar form of the complex number $z=2-2\sqrt{3}i$?
  • 2014 E.C., Q20 – Which of the following is true about the trigonometric values of $855^\circ$?
  • 2014 E.C., Q21 – Which one of the following is true about the function y = sin x?
  • 2014 E.C., Q44 – Which one of the following trigonometric values is correct?
4.4 Application · read p. 207
Not asked in a national paper yet.
4.3 Trigonometric Identities & Equation…… · read p. 234
  • 2018 E.C., Q14 – If $\cos\theta=-\frac{5}{13}$ and $\theta$ is an angle in the second quadrant, then what is the value of $\cot\theta$?
  • 2018 E.C., Q15 – If $\cos \theta = -\frac{5}{13}$ and $\theta$ is an angle in the second quadrant, then what is the value of $\cot \theta$?
  • 2018 E.C., Q29 – Let $P(a,b)$ be a point, other than the origin $(0,0)$, on the terminal side of an angle $\theta$ in standard position. Then what is the value of $\cos\theta$?
  • 2018 E.C., Q52 – If $\alpha$ and $\beta$ are complementary angles ($\alpha + \beta = 90^\circ$), which of the following trigonometric relations is always true?
  • 2017 E.C., Q47 – Let $\theta$ be an angle in standard position and $(x, y)$ be a point on the terminal side of $\theta$, which is different from the origin. Let $r$ be the distance from $(x, y)$ to the origin. Then which of the following
  • 2016 E.C., Q12 – Let $\theta$ be an angle in standard position and $P(-3, 4)$ be a point on the terminal side of $\theta$. Which one of the following is true about the corresponding trigonometric functions?
  • 2016 E.C., Q22 – Which of the following is true about a trigonometric value of angles?
  • 2016 E.C., Q14 – For , which of the following identity is correct? csc (90 − 2 ∘ θ) = 1 + tan θ 2 cot (90 − 2 ∘ θ) = 1 + csc θ 2
  • 2015 E.C., Q11 – If tan31° = 0.81 then what is the value of tan509°
  • 2015 E.C., Q49 – Let $f(x)=3x+2x-\sin x+e^x$. What is the value of $f'(0)$?
  • 2015 E.C., Q3 – Which one of the following is true for the values of the trigonometric functions for the indicated angles?
  • 2014 E.C., Q28 – What is the derivative of the function $f(x)=\frac{xe^x}{\cos x}$ at $x=0$?
  • 2014 E.C., Q9 – The angle of depression of the top of a flag pole from the top of a building that is 40.3 m away from the flag pole is 30°. If the height of the flag pole is 10m, what is the height of the building?
  • 2014 E.C., Q13 – Which one of the following is the derivative of f(x) = tanx + 3 x ?
  • 2013 E.C., Q25 – Which of the following functions represents the graph shown in Figure 2?
  • 2013 E.C., Q42 – Which of the following is equal to $\int (\cos x - 2x)\, \mathrm{d}x$ where $c$ is a constant?
  • 2013 E.C., Q60 – The angle of elevation of the top of a tree is found to be 60° as measured from a point on a level ground. What is the height of the tree if the angle of elevation of a point on the tree that is 8m below the top is 30° a