The equation 2^2 x = 1 has four solutions in 0 x < 2π. What is their sum?

Worked solution for TMUA-P1-MM4-012 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MM4-012 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM4-012 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM4-012?

No — calculators are banned in the TMUA. TMUA-P1-MM4-012 is set for a no-calculator target of about 240 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM4-012?

TMUA-P1-MM4-012 is Paper P1 · Trigonometry (specification code MM4), level 3. Drill more of the same topic from this page.

TMUA-P1-MM4-012 — Paper P1 · Trigonometry · Level 3

Q: Why isn't the answer to TMUA-P1-MM4-012 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM4-012 first — TMUA questions reward spotting the trap before you check the worked solution below.

Q: Do I need a calculator for TMUA-P1-MM4-012?

No — calculators are banned in the TMUA. TMUA-P1-MM4-012 is set for a no-calculator target of about 240 seconds; the worked solution shows the fastest by-hand route.

Q: Which TMUA specification point is TMUA-P1-MM4-012?

TMUA-P1-MM4-012 is Paper P1 · Trigonometry (specification code MM4), level 3. Drill more of the same topic from this page.

P1MM4Level 3~240s target

Spec: MM4 · No calculator · ~240s

The equation

2\sin^2 x = 1

has four solutions in

0 \le x < 2\pi

. What is their sum?

Options

$\pi$
$2\pi$
$3\pi$
$4\pi$
$8\pi$

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: squared-trig-equation, dropped-negative-branch. Name the trap first, work the stem by hand, then open the solution below.

Show solution

\sin^2 x = \frac{1}{2}

gives

\sin x = \pm\frac{1}{\sqrt{2}}

, one solution per quadrant:

\frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}

. Their sum is

\frac{16\pi}{4} = 4\pi

. Trap:

2\pi

counts only the two positive-branch solutions — plausible if you drop the

\pm

Keep practising

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P2PRF4Level 2
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Keep practising

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: dropped-negative-branch

P2PRF4Level 2

TMUA-P2Y-PRF-013

Disprove the claim: for all integers a and b, if a^2 = b^2 then a = b.

Disproof by counterexample

Open TMUA-P2Y-PRF-013 →

TMUA-P1-MM4-012 — Paper P1 · Trigonometry · Level 3

Options

Keep practising

Master Trigonometry

TMUA-P1-MM4-012 — Paper P1 · Trigonometry · Level 3

Options

Keep practising

Master Trigonometry