Give the value of each trigonometric ratio: a)cos (-390degrees)`` b) tan 45          c) sin 270 degrees,      d) sin (`(5pi)/6` ) ````Please explain 

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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In trigonometry we know that;

`cos(-theta) = costheta`

`cos(360+theta) = costheta`

`sin(pi-theta) = sintheta`

`sin(180+theta) = -sintheta`

 

Generally we know the following trigonometric values.

                     sin                 cos               tan

`0`                    `0`                   ` 1`                   ` 0`

`30 ` or `pi/6`          `1/2`                  ` sqrt3/2`                 `1/sqrt3`

`45` or `pi/4`       `1/sqrt2`                `1/sqrt2`                   `1`

`60` or `pi/3`        ` sqrt3/2`                    ` 1/2`                  `sqrt3`

`90` or `pi/2`         `1`                      `0`                  `oo`

 

 

So the answers can be derived as follows.

`cos(-390) = cos390 = cos(360+30) = cos30 = sqrt3/2`

 

`tan45 = 1`

 

`sin270 = sin(180+90) = -sin90 = -1`

 

`sin((5pi)/6) = sin(pi-pi/6) = sin(pi/6) = 1/2`

 

Sources:

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