EmSAT Achieve (UAE) · Mathematics

Trigonometry, Vectors and Complex Numbers

29 practice questions, each with the answer and an explanation.

Practise Trigonometry, Vectors and Complex Numbers now

Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 29 questions

What is the exact value of $cos (\frac{5 π}{6})$ ?
What is the dot product of the vectors $u = ⟨ 3, - 4 ⟩$ and $v = ⟨ 5, 2 ⟩$ ?
What is the angle $θ$ between two non-zero vectors $a$ and $b$ if $a \cdot b = 0$ ?
Simplify the complex number $\frac{4 + 2 i}{1 - i}$ , where $i^{2} = - 1$ .
What is the exact value of $sin (2 θ)$ if $sin θ = \frac{3}{5}$ and $θ$ lies in Quadrant I?
What is the magnitude of the 3D vector $w = ⟨ 2, - 3, 6 ⟩$ ?
Which expression is identically equal to $\frac{1 - c o s ( 2 x )}{2}$ ?
In triangle $A B C$ , $a = 5$ , $b = 8$ , and $c = 7$ . What is the measure of angle $C$ ?
What is the polar form of the complex number $z = 1 + i 3$ ?
What is the unit vector in the direction of $v = ⟨ 6, - 8 ⟩$ ?
What is the value of $cos (7 5^{\circ})$ using sum and difference identities?
Evaluate $(1 + i)^{8}$ , where $i^{2} = - 1$ .
What is the area of a triangle with sides $a = 6$ , $b = 10$ , and included angle $C = 3 0^{\circ}$ ?
Which vector is orthogonal (perpendicular) to $u = ⟨ 4, - 6 ⟩$ ?
What is the value of $tan (2 θ)$ if $tan θ = \frac{1}{3}$ ?
What is the real part of $\frac{1}{3 + 4 i}$ ?
What is the solution to $cos (x) = - \frac{1}{2}$ on the interval $[0, 2 π)$ ?
If $a = 2 \hat{i} + 3 \hat{j}$ and $b = - \hat{i} + 4 \hat{j}$ , what is $∣2 a - b ∣$ ?
Which trigonometric identity is correct for all real $x$ where functions are defined?
What is the projection of vector $u = ⟨ 2, 3 ⟩$ onto vector $v = ⟨ 4, 0 ⟩$ ?
What is the exact value of $sin (- \frac{π}{4}) + cos (\frac{3 π}{4})$ ?
If $z = 3 - 4 i$ , what is $z \cdot \overset{z}{ˉ}$ (where $\overset{z}{ˉ}$ is the complex conjugate of $z$ )?
What is the cross product magnitude $∣ u \times v ∣$ if $∣ u ∣ = 5$ , $∣ v ∣ = 8$ , and the angle between them is $3 0^{\circ}$ ?
In a right triangle $A B C$ with right angle at $C$ , if $tan A = \frac{5}{12}$ , what is $csc A$ ?
What is the volume of the solid generated by revolving $y = x$ about the x-axis from $x = 0$ to $x = 4$ ?
Evaluate $lim_{x \to \infty} (1 + \frac{3}{x})^{2 x}$ .
What is the derivative $\frac{d y}{d x}$ if $x^{2} + y^{2} = 25$ evaluated at the point $(3, 4)$ ?
A committee of 4 people is chosen from 5 men and 6 women. What is the probability that the committee contains exactly 2 men and 2 women?
What is the distance from the point $P (1, 2, 3)$ to the plane $2 x - 2 y + z + 5 = 0$ ?

Trigonometry, Vectors and Complex Numbers

Practise Trigonometry, Vectors and Complex Numbers now

All 29 questions

Keep practising

More EmSAT Achieve (UAE) topics

Ready for the full EmSAT Achieve (UAE) test?