If θ = 3/5 with θ acute, find θ.

Worked solution for TMUA-P1-MM4-016 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MM4-016 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM4-016 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM4-016?

No — calculators are banned in the TMUA. TMUA-P1-MM4-016 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-MM4-016?

TMUA-P1-MM4-016 is Paper P1 · Trigonometry (specification code MM4), level 2. Drill more of the same topic from this page.

TMUA-P1-MM4-016 — Paper P1 · Trigonometry · Level 2

P1MM4Level 2~150s target

Spec: MM4 · No calculator · ~150s

\sin\theta = \frac{3}{5}

with

\theta

acute, find

\cos\theta

Options

$\frac{4}{5}$
$\frac{3}{4}$
$\frac{5}{4}$
$\frac{2}{5}$

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: pythagorean-identity, acute-angles. Name the trap first, work the stem by hand, then open the solution below.

Show solution

\cos^2\theta = 1 - \frac{9}{25} = \frac{16}{25}

, and

\cos\theta > 0

for acute

\theta

, so

\cos\theta = \frac{4}{5}

and the correct is A. Trap:

\frac{3}{4}

divides

3

4

instead of using Pythagoras.

Keep practising

Same topic · same level
P1MM4Level 2
TMUA-P1-MM4-005
A triangle has sides of length 5 and 7 with included angle 60^°. What is the length of the third side?
Trigonometry
Open TMUA-P1-MM4-005 →
Same trap: pythagorean-identity
P1MM4Level 2
TMUA-P1-MM4-009
The angle θ is acute and θ = 5/13. What is the value of θ?
Trigonometry
Open TMUA-P1-MM4-009 →
Step up a 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 →

Browse more

Loading…

Keep practising

Same topic · same level

P1MM4Level 2

TMUA-P1-MM4-005

A triangle has sides of length 5 and 7 with included angle 60^°. What is the length of the third side?

Trigonometry

Open TMUA-P1-MM4-005 →

Same trap: pythagorean-identity

P1MM4Level 2

TMUA-P1-MM4-009

The angle θ is acute and θ = 5/13. What is the value of θ?

Trigonometry

Open TMUA-P1-MM4-009 →

Step up a 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 →

TMUA-P1-MM4-016 — Paper P1 · Trigonometry · Level 2

Options

Keep practising

Master Trigonometry

TMUA-P1-MM4-016 — Paper P1 · Trigonometry · Level 2

Options

Keep practising

Master Trigonometry