Question

A point on the terminal side of an angle theta in standard position is (negative 24 comma 10 ). Find the exact value of each of the six trigonometric functions of theta.

Answer 1

`sin \theta=\frac5{13}`

`cos\theta=-(12)/(13)`

`tan\theta =-(5)/(12)`

`cec \theta=2(3)/(5)`

`sec\theta=-1\frac1{12}`

`cot \theta=-2(2)/(5)`

Explanation:

Given point is (-24,10)

The distance between given point and the origin is

`r=√(x^2+y^2)`

Here r
`=√((-24)^2+(10)^2)`

=26 units.

x= -24 and y= 10

Now 6 trigonometric functions are

`sin \theta=\frac yr=(10)/(26)=\frac5{13}`

`cos\theta=(x)/(r)=(-24)/(26)=-(12)/(13)`

`tan\theta =(y)/(x)=(10)/(-24)=-(5)/(12)`

`cec \theta= (r)/(y)=(26)/(10)=(13)/(5)=2(3)/(5)`

`sec\theta=\frac rx=(26)/(-24)=-(13)/(12)=-1\frac1{12}`

`cot \theta=(x)/(y)=(-24)/(10)=-(12)/(5)=-2(2)/(5)`