The value of sin(11π)/(6) is:

sin (2π - (π)/(6)) = -sin(π)/(6) = -(1)/(2).

The point on the unit circle associated with x = (7π)/(4) lies in:

(7π)/(4) ∈ ((3π)/(2), 2π), which is the fourth quadrant.

The number of solutions of sin x = -(1)/(2) on [0, 2π) is:

sin x = -(1)/(2) at x = (7π)/(6) (Q3) and x = (11π)/(6) (Q4). Two solutions on [0, 2π).

The value of tan(7π)/(6) is:

tan (π + (π)/(6)) = tan(π)/(6) = (1)/(√(3)).

The value of cos (-(π)/(3)) is:

cos (-(π)/(3)) = cos(π)/(3) = (1)/(2).

The exact value of sin ((π)/(6)) is:

(π)/(6) = 30°, and sin 30° = (1)/(2).

The value of sin(π)/(6) is:

A standard unit-circle value: sin(π)/(6) = (1)/(2).

For x = (2π)/(3), the sign of sin x is:

In the second quadrant (π/2 0.

The value of cos(π)/(4) is:

cos(π)/(4) = sin(π)/(4) = (√(2))/(2).

The value of tan(π)/(3) is:

tan(π)/(3) = (sin(π/3))/(cos(π/3)) = (√(3)/2)/(1/2) = √(3).

IB Maths AA

Practice by topic

The unit circle and circular functions practice questions — IB Maths AA

12 free multiple-choice problems on the unit circle and circular functions, ordered to match IB Maths AA difficulty, each with a full worked solution. No account needed — and there's a fresh problem set every day.

Try 3 problems from this chapter

1 / 3

Problem #0555 International

Mediumtrigonometry

The value of is:

Problems & worked solutions

Problem #0555 International

Problem 1 — The unit circle and circular functions

The value of $\sin \frac{11 π}{6}$ is:

Show answer & worked solution

A. $\frac{1}{2}$
B. $- \frac{1}{2}$ ✓ correct
C. $\frac{\sqrt{3}}{2}$
D. $- \frac{\sqrt{3}}{2}$

$\sin ⁣ (2 π - \frac{π}{6}) = - \sin \frac{π}{6} = - \frac{1}{2}$ .

Problem #0557 International

Problem 2 — The unit circle and circular functions

The point on the unit circle associated with $x = \frac{7 π}{4}$ lies in:

Show answer & worked solution

A. $the first quadrant$
B. $the second quadrant$
C. $the third quadrant$
D. $the fourth quadrant$ ✓ correct

$\frac{7 π}{4} \in ⁣ (\frac{3 π}{2}, 2 π)$ , which is the fourth quadrant.

Problem #0559 International

Problem 3 — The unit circle and circular functions

The number of solutions of $\sin x = - \frac{1}{2}$ on $[0, 2 π)$ is:

Show answer & worked solution

A. $1$
B. $2$ ✓ correct
C. $3$
D. $4$

$\sin x = - \frac{1}{2}$ at $x = \frac{7 π}{6}$ (Q3) and $x = \frac{11 π}{6}$ (Q4). Two solutions on $[0, 2 π)$ .

Problem #0558 International

Problem 4 — The unit circle and circular functions

The value of $\tan \frac{7 π}{6}$ is:

Show answer & worked solution

A. $\frac{1}{\sqrt{3}}$ ✓ correct
B. $- \frac{1}{\sqrt{3}}$
C. $\sqrt{3}$
D. $- \sqrt{3}$

$\tan ⁣ (π + \frac{π}{6}) = \tan \frac{π}{6} = \frac{1}{\sqrt{3}}$ .

Problem #0556 International

Problem 5 — The unit circle and circular functions

The value of $\cos ⁣ (- \frac{π}{3})$ is:

Show answer & worked solution

A. $\frac{1}{2}$ ✓ correct
B. $- \frac{1}{2}$
C. $\frac{\sqrt{3}}{2}$
D. $- \frac{\sqrt{3}}{2}$

$\cos ⁣ (- \frac{π}{3}) = \cos \frac{π}{3} = \frac{1}{2}$ .

Problem #0945 US SAT

Problem 6 — The unit circle and circular functions

The exact value of $\sin ⁣ (\frac{π}{6})$ is:

Show answer & worked solution

A. $\frac{1}{2}$ ✓ correct
B. $\frac{\sqrt{2}}{2}$
C. $\frac{\sqrt{3}}{2}$
D. $1$

$\frac{π}{6} = 30^{\circ}$ , and $\sin 30^{\circ} = \frac{1}{2}$ .

Problem #0551 International

Problem 7 — The unit circle and circular functions

The value of $\sin \frac{π}{6}$ is:

Show answer & worked solution

A. $\frac{1}{2}$ ✓ correct
B. $\frac{\sqrt{2}}{2}$
C. $\frac{\sqrt{3}}{2}$
D. $1$

A standard unit-circle value: $\sin \frac{π}{6} = \frac{1}{2}$ .

Problem #0554 International

Problem 8 — The unit circle and circular functions

For $x = \frac{2 π}{3}$ , the sign of $\sin x$ is:

Show answer & worked solution

A. $positive$ ✓ correct
B. $negative$
C. $zero$
D. $undefined$

In the second quadrant ( $π / 2 < x < π$ ), $\sin x > 0$ .

Problem #0552 International

Problem 9 — The unit circle and circular functions

The value of $\cos \frac{π}{4}$ is:

Show answer & worked solution

A. $\frac{1}{2}$
B. $\frac{\sqrt{2}}{2}$ ✓ correct
C. $\frac{\sqrt{3}}{2}$
D. $1$

$\cos \frac{π}{4} = \sin \frac{π}{4} = \frac{\sqrt{2}}{2}$ .

Problem #0553 International

Problem 10 — The unit circle and circular functions

The value of $\tan \frac{π}{3}$ is:

Show answer & worked solution

A. $\frac{1}{\sqrt{3}}$
B. $1$
C. $\sqrt{3}$ ✓ correct
D. $\frac{\sqrt{3}}{2}$

$\tan \frac{π}{3} = \frac{\sin (π / 3)}{\cos (π / 3)} = \frac{\sqrt{3} / 2}{1 / 2} = \sqrt{3}$ .

2 more The unit circle and circular functions questions in the app

Also covered in The unit circle and circular functions practice across every exam.

Not sure where you stand? Take the free 10-question placement test — no account, ~15 minutes.