Trigonometry - Basics

We use the Unit Circle to construct the sine and the cosine functions. The unit circle is called like this because:

• It is only one circle

• The area of the circle is equal to one

• Because its radius is equal to one

• Because its circumference is equal to one

Tags

CCSS.HSF.TF.A.2

The Unit Circle has four quadrants such that:

• All quadrants have 90 degrees

• Quadrant IV is between π and 3π/2 radians

• Quadrant III is between 3π/2 and 2π and radians

• Quadrant I is where the acute angles are

Tags

CCSS.HSF.TF.A.2

In quadrant III (three):

• sinx < 0 ; cos x > 0; tan <0

• sinx > 0 ; cos x > 0; tan >0

• sinx < 0 ; cos x < 0; tan >0

• sinx > 0 ; cos x < 0; tan <0

Tags

CCSS.HSF.TF.A.2

The value of cos(-π/6) is

• √2/2

• √3/2

• 1/2

• -1/2

The value of sin(7π/6) is

• 1/2

• -1/2

• -√3/2

• -√2/2

The value of cos(-240⁰) is

• 0.5

• -0.5

• -0.866

• -0.707

The value of cos(765^o) is

• -0.707

• 0.707

• -0.5

• 0.5

The value of cos (690^o) is

• -0.707

• -0.866

• 0.866

• -0.5

The following statements ARE true:

• sin(330^o)=sin(240⁰)

• sin(-390^o)=sin(150⁰)

• sin(930^o)=-sin(390⁰)

• sin(-360^o)=sin(7200⁰)

The following ARE true:

• sin(150^o)=cos(60^o)

• sin(210^o)=cos(120^o)

• cos(150^o)=sin(60^o)

• cos(45^o)=sin(-45^o)