Solve x = -1/2 for 0^° < x < 360^°.

Worked solution for TMUA-P1-MM4-019 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MM4-019 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM4-019 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM4-019?

No — calculators are banned in the TMUA. TMUA-P1-MM4-019 is set for a no-calculator target of about 150 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM4-019?

TMUA-P1-MM4-019 is Paper P1 · Trigonometry (specification code MM4), level 3. Drill more of the same topic from this page.

TMUA-P1-MM4-019 — Paper P1 · Trigonometry · Level 3

Q: Why isn't the answer to TMUA-P1-MM4-019 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM4-019 first — TMUA questions reward spotting the trap before you check the worked solution below.

Q: Do I need a calculator for TMUA-P1-MM4-019?

No — calculators are banned in the TMUA. TMUA-P1-MM4-019 is set for a no-calculator target of about 150 seconds; the worked solution shows the fastest by-hand route.

Q: Which TMUA specification point is TMUA-P1-MM4-019?

TMUA-P1-MM4-019 is Paper P1 · Trigonometry (specification code MM4), level 3. Drill more of the same topic from this page.

P1MM4Level 3~150s target

Spec: MM4 · No calculator · ~150s

Solve

\cos x = -\frac{1}{2}

for

0^\circ < x < 360^\circ

Options

$60^\circ$ and $300^\circ$
$120^\circ$ and $240^\circ$
$150^\circ$ and $210^\circ$
$135^\circ$ and $225^\circ$

Letters only — the answer key is hidden. Work it out, then check the solution below.

Hint (check trope)

No written hint yet — check the trope: trig-equations, cast-quadrants. Name the trap first, work the stem by hand, then open the solution below.

Show solution

\cos x = -\frac{1}{2}

is negative in quadrants II and III:

x = 180^\circ \pm 60^\circ = 120^\circ, 240^\circ

, so the correct is B. Trap:

60^\circ

and

300^\circ

solve

\cos x = \frac{1}{2}

, missing the negative sign.

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Same topic · same level

P1MM4Level 3

TMUA-P1-MM4-011

A triangle has sides of length 4, 5 and 6. What is the cosine of its largest angle?

Trigonometry

Open TMUA-P1-MM4-011 →

Same trap: trig-equations

P1MM4Level 2

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Solve x = √32 for 0^° < x < 90^°.

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Open TMUA-P1-MM4-014 →

TMUA-P1-MM4-019 — Paper P1 · Trigonometry · Level 3

Options

Keep practising

Master Trigonometry

TMUA-P1-MM4-019 — Paper P1 · Trigonometry · Level 3

Options

Keep practising

Master Trigonometry