`510^@` Evaluate the sine, cosine and tangent of the angle without using a calculator.

Textbook Question

Chapter 4, 4.4 - Problem 58 - Precalculus (3rd Edition, Ron Larson).
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kspcr111 | In Training Educator

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1)

`sin(510^@) = sin(360^@+150^@) `

As we know that `sin(360^@+x^@) = sin(x^@)`

so ,

`sin(360^@+150^@) = sin(150^@) `
 
`= sin(180 - 30) =sin(30) = 1/2`

2)

`cos(510^@) = cos(360^@+150^@)`

As we know that `cos(360^@+x^@) = cos(x^@)

`

so,

`cos(360^@ +150^@) = cos(150^@)`

 `= cos(180-30) = -cos(30) = - sqrt(3)/ 2`

3)

`Tan(510^@)= (sin(510^@))/(cos(510^@)) = (1/2)/(- sqrt(3)/ 2) = -(1/sqrt(3))`

 

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