Precalc +: Terminal Point Trigonometry

Radius is equal to

√x^2 + y^2, where (x,y) is a point on the terminal side of an angle Θ in standard point (always positive)

Sin (Θ)

y/r

Cos (Θ)

x/r

Tan (Θ)

y/x

Csc (Θ)

r/y

Sec (Θ)

r/x

Cot (Θ)

x/y

Terminal Point

Point on a terminal ray that intersects the circle

Sin (0°)

0

Cos (0°)

1

Tan (0°)

0

Csc (0°)

Undefined

Sec (0°)

1

Cot (0°)

Undefined

Sin (90°)

1

Cos (90°)

0

Tan (90°)

Undefined

Csc (90°)

1

Sec (90°)

Undefined

Cot (90°)

0

Trig Ratios for angles above 90° or below 0°

Same as the Trig Ratio for the reference angle, but the signs for the ratio change. (+/-x, +/-y) have the same radii, and therefore have the same trig ratios, just with different signs.

All Students Take Calculus

Acronym used to remember which Trigonometric functions are positive in which quadrant. In quadrant 1, __a__ll ratios are positive. In quadrant 2, __s__ine and its reciprocal function cosecant are positive. In quadrant 3, __t__angent and its reciprocal function cotangent are positive. In quadrant 4, __c__osine and its reciprocal function secant are positive.

Sin (180°)

0

Cos (180°)

\-1

Tan (180°)

0

Csc (180°)

Undefined

Sec (180°)

\-1

Cot (180°)

Undefined

Sin (270°)

\-1

Cos (270°)

0

Tan (270°)

Undefined

Csc (270°)

\-1

Sec (270°)

Undefined

Cot (270°)

0