S5 Mathematics

sin θ = opposite / hypotenuse.

cos θ = adjacent / hypotenuse.

tan θ = opposite / adjacent.

Side opposite angle θ.

Side next to angle θ (not hypotenuse).

Longest side, opposite right angle.

30°, 45°, 60°, have exact values.

Sin=opp/hyp, Cos=adj/hyp, Tan=opp/adj.

Angle from horizontal line looking up, e.g. look at mountain top.

Angle from horizontal line looking down, e.g. from mountain top look down.

Angle clockwise from north, three digits, e.g. 045°.

Line parallel to ground.

Line perpendicular to ground, up down direction.

Right triangle formed after draw diagram.

Draw diagram, find right triangle, use trig ratio calculate answer.

Length between two points.

Distance from center to circumference, r.

Through center, both ends on circumference, twice radius.

Line segment between two points on circle.

Curved part on circumference.

Vertex at center, sides to circumference.

Vertex on circumference, sides to circumference.

π ≈ 3.14159, circumference = πd = 2πr.

Circle area = πr².

(x, y) represents a point on plane.

Length between two points, use distance formula.

Point exactly middle between two points.

Line slope, = rise / run.

y = mx + c, m slope, c y-intercept.

Point where line intersects axis.

Two lines same slope.

Two lines slope multiply = -1.

y directly proportional to x, y = kx.

y inversely proportional to x, y = k/x.

y directly x, inversely z, y = kx/z.

Proportional constant k, need to find.

One changes, other changes same ratio.

1/x, e.g. reciprocal of 2 is 12.

Numbers given in problem, used to find k.

After find k, substitute other numbers find unknown.

Space solid takes up.

All surface area of solid.

Two parallel polygon faces, sides rectangles.

Two parallel circular faces, side curved.

Base polygon, top one point.

Base circle, top one point.

Round solid, e.g. ball.

Area of solid base.

(x - h)² + (y - k)² = r², (h,k) center, r radius.

x² + y² + Dx + Ey + F = 0.

Center point of circle, (h, k).

Distance from center to circumference, r.

Method change general form back to standard.

Standard form, directly see center and radius.

Substitute point, if satisfy then on circle.

(0, 0) coordinate center.

Difference between measured and true value.

Absolute error / true value.

Relative error × 100%.

Number measured with tool.

Actual accurate number.

What each mark on measuring tool represents.

Half of scale interval.

How accurate measurement is.

The tilt of a line.

y-y₁=m(x-x₁).

Ax+By+C=0.

Equal slopes.

Slopes multiply to -1.

Where the line crosses the y-axis.

Solved to find the intersection.

Geometry with coordinates.

The repeat length: 360° for sin and cos.

Maximum distance from the mean line.

Both peak at 1.

Both bottom out at -1.

The acute angle from the calculator.

Quadrants decide the sign.

Equations with two solutions per cycle.

Describing periodic phenomena mathematically.