Trigonometry Reviewer 1st Quarter
Trigonometry Reviewer 1st Quarter
Trigonometry Reviewer 1st Quarter
Degree Measure
Trigonometric Function on Quadrantal Angles
Degree (°) –most common unit for measuring angles
Portions of a degree have been measured with minutes
sinΘ cosΘ tanΘ cscΘ secΘ cotΘ
and seconds
One minute (1’) is 1/60 of a degree 0° 0 1 0 Undef. 1 Undef.
One second (1”) is 1/60 of a minute 90° 1 0 Undef. 1 Undef. 0
180° 0 -1 0 Undef. -1 Undef.
Degree, Minute, Second to Decimal Degree
270° -1 0 Undef. -1 Undef. 0
Ex. 80°45’ = 80.75°
360° 0 1 0 Undef. 1 Undef.
45’/60 = .75
Decimal Degree to Degree, Minute, Second
Ex. 120. 38° = 120°22’48” Reciprocal Indentities
.38*60 = 22.8
.8*60 = 48 1. sinΘ = 1/ cscΘ
2. cosΘ = 1/ secΘ
Standard Position and Coterminal Angles
Standard Postion- its vertex at the origin and its initial 3. tanΘ = 1/ cotΘ
side lies on the positive x-axis 4. cscΘ = 1/ sinΘ
Quadrantal Angles – terminal side on x-axis or y-axis
5. secΘ = 1/ cosΘ
6. cotΘ = 1/ tanΘ
Quadrant II Quadrant I
Pythagorean Identities
x² + y² = r²
Quadrant III Quadrant IV
1. 1 + tan²Θ = sec²Θ
2. cot²Θ + 1 = csc²Θ
3. cos²Θ + sin²Θ = 1
Reference Angles
Cofunction positive acute angle
value for the compliment of an angle is equal to the value x-axis + terminal side
of a given trigonometric function of the angle itself
r
y
A x
If A increases…
sin A, tan A, sec A - increases
cos A, csc A, cot A - decreases QII – Θ’ = 180° - Θ
2 2
√33 √2223
QIII – Θ’ = Θ - 180°
1
√23
sin 30 = 1/2
cos 30 = √3/2
tan 30 = √3/3
REVIEWER IN GEOMETRY
1ST QUARTER: TRIGONOMETRIC FUNCTIONS/ ACUTE AND NON-ACUTE
ANGLES AND RIGHT TRIANGLES
object
angle greater than 0° but less than 360°
2. Find the reference angles horizontal line
observer
3. Find the trigonometric function values for refernce angles.
4. Determine the correct signs for the values function step 3.
Find the values of the six trigonometric functions
b -Abaya, 10-E