Are these Triangles and Trigonometry notes free?

Yes. The full 3-page Triangles and Trigonometry sheet is free inside CapCompass, which runs in your browser with no account needed.

What does the Triangles and Trigonometry revision sheet cover?

Every ratio is measured from ONE angle, The five lines this whole topic runs on, sine of the marked angle, cosine, tangent, Pythagoras, with c the hypotenuse, complementary angles, the one identity you need, Worked: sine, cosine and the complement, The two special triangles, both printed on the sheet, 45-45-90, 30-60-90, Worked: a triple you should recognise.

Is this for Digital SAT SAT Math?

Yes, it is written for the Digital SAT SAT Math syllabus.

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Triangles and Trigonometry — Digital SAT SAT Math revision notes

A 3-page visual revision sheet for Triangles and Trigonometry, written for Digital SAT SAT Math. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.

Triangles and Trigonometry revision notes, page 1 of 3 — A preview of page 1 — all 3 pages open full size in the app.

Triangles and Trigonometry in one look

three ratios, two special shapes, and a list of triples worth knowing

Every ratio is measured from ONE angle

opposite and adjacent are not properties of a side. They are relative to the angle you picked, and they swap the moment you switch to the other acute angle
the hypotenuse never swaps. It is the longest side and it always faces the 90 degree corner
SOH CAH TOA: Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, Tangent is Opposite over Adjacent
the two acute angles of a right triangle add to 90, which is why the sine of one equals the cosine of the other

The five lines this whole topic runs on

sine of the marked angle sin x=opp/hyp
cosine cos x=adj/hyp
tangent tan x=opp/adj
Pythagoras, with c the hypotenuse a^2+b^2=c^2
complementary angles, the one identity you need sin x=cos(90°-x)

Worked: sine, cosine and the complement

Q. in triangle PQR the angle at Q measures 90°. If sin(P)=4/5, what is cos(R)?

the three angles total 180 and Q takes 90, so P+R=90. The two acute angles are complementary
that makes R=90°-P
cos(R)=cos(90°-P), and cosine of the complement is sine of the angle itself
so cos(R)=sin(P)=4/5

Answer: cos(R)=4/5

Page 1 of 3. The full sheet, all 3 pages, opens free in the app.

What this Triangles and Trigonometry sheet covers

Every ratio is measured from ONE angle
The five lines this whole topic runs on
sine of the marked angle
cosine
tangent
Pythagoras, with c the hypotenuse
complementary angles, the one identity you need
Worked: sine, cosine and the complement
The two special triangles, both printed on the sheet
45-45-90
30-60-90
Worked: a triple you should recognise
Which tool does this question want
Symbols and terms
Worked: all three ratios at once
Pacing, the sheet and the calculator
Traps that cost points
Tricks that save time

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